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transformation, not the starting shape. The original shape before transformation is called the object."},{"text":"The vector.","correct":false,"explanation":"A vector describes the direction and distance of a translation; it does not name a shape. The starting shape is called the object."},{"text":"The centre.","correct":false,"explanation":"A centre may identify the fixed point of a rotation or enlargement, rather than the starting shape. The starting shape is called the object."}]},{"id":"9e576a52-48b9-d451-00de-baf4eac070b3","cardType":"basic","points":1,"front":"In transformations, what is the name for the shape after it has been moved or resized?","back":"The image.","mcqOptions":[{"text":"The image.","correct":true,"explanation":"The image is the resulting shape after the object has been translated, reflected, rotated or enlarged by a transformation."},{"text":"The object.","correct":false,"explanation":"The object is the original shape before the transformation takes place. The shape produced after it has been transformed is called the image."},{"text":"The vector.","correct":false,"explanation":"A vector specifies the movement in a translation, rather than naming the transformed shape. The resulting shape is called the image."},{"text":"The centre.","correct":false,"explanation":"A centre is a point used to define a rotation or enlargement, not the transformed shape. The shape produced is called the image."}]},{"id":"8346d2fb-c9b7-d765-0c94-9d318605d51e","cardType":"basic","points":1,"front":"In a translation vector, what movement does a negative top number indicate?","back":"Movement to the left.","mcqOptions":[{"text":"Movement to the left.","correct":true,"explanation":"The top number of a translation vector controls horizontal movement, and a negative value means movement to the left."},{"text":"Movement to the right.","correct":false,"explanation":"A positive top number represents movement to the right. A negative top number reverses the horizontal direction, so it indicates movement to the left."},{"text":"Movement to the up.","correct":false,"explanation":"Vertical movement is controlled by the bottom number, not the top number. A negative top number represents horizontal movement to the left."},{"text":"Movement to the down.","correct":false,"explanation":"A negative bottom number would indicate movement down. The top number controls horizontal movement, so a negative top number means left."}]},{"id":"87ff2314-4e87-7521-0fe7-c8009379648c","cardType":"basic","points":1,"front":"In a translation vector, what movement does a positive bottom number indicate?","back":"Movement up.","mcqOptions":[{"text":"Movement up.","correct":true,"explanation":"The bottom number of a translation vector controls vertical movement, and a positive value means movement upwards."},{"text":"Movement down.","correct":false,"explanation":"A negative bottom number represents downward movement. Since the bottom number is positive, the translation instead moves vertically upwards."},{"text":"Movement right.","correct":false,"explanation":"Horizontal movement is determined by the top number of the vector. A positive bottom number controls vertical movement and therefore means up."},{"text":"Movement left.","correct":false,"explanation":"Movement to the left is represented by a negative top number. A positive bottom number instead indicates vertical movement upwards."}]},{"id":"9c540889-85af-a6bc-d132-794a017c090e","cardType":"basic","points":1,"front":"What detail is required to describe a translation fully?","back":"A vector $\\begin{pmatrix} x \\\\ y \\end{pmatrix}$.","mcqOptions":[{"text":"A vector $\\begin{pmatrix} x \\\\ y \\end{pmatrix}$.","correct":true,"explanation":"A translation is fully described by a column vector, where $x$ gives horizontal movement and $y$ gives vertical movement."},{"text":"A coordinate $(x, y)$.","correct":false,"explanation":"A coordinate locates one point and does not describe how every point moves. A translation requires a vector giving horizontal and vertical displacement."},{"text":"A scale factor $k$.","correct":false,"explanation":"A scale factor is required for an enlargement, not a translation. A translation is fully specified by a vector showing horizontal and vertical movement."},{"text":"A line $y=mx+c$.","correct":false,"explanation":"A line is needed to describe the mirror line of a reflection, not a translation. A translation must be described using a vector."}]},{"id":"69deda4f-e1e2-a98f-db6e-e130fc93ba06","cardType":"basic","points":1,"front":"When reflecting a point in the $x$-axis, how do the coordinates change?","back":"The $y$-coordinate changes sign (multiplied by -1).","mcqOptions":[{"text":"The $y$-coordinate changes sign (multiplied by -1).","correct":true,"explanation":"Reflection in the $x$-axis reverses a point’s vertical position, so the $y$-coordinate changes sign while the $x$-coordinate remains unchanged."},{"text":"The $x$-coordinate changes sign (multiplied by -1).","correct":false,"explanation":"Changing the $x$-coordinate reflects a point in the $y$-axis. Reflection in the $x$-axis instead changes the sign of the $y$-coordinate."},{"text":"The $x$- and $y$-coordinates change sign (multiplied by -1).","correct":false,"explanation":"Changing both signs gives a half-turn about the origin, not a reflection in the $x$-axis. Only the $y$-coordinate changes sign."},{"text":"The $y$-coordinate stays unchanged (multiplied by 1).","correct":false,"explanation":"Leaving the $y$-coordinate unchanged would not reverse the point’s vertical position. Reflection in the $x$-axis changes the sign of the $y$-coordinate."}]},{"id":"3c8ec916-f041-0290-1b94-6bd6947b4150","cardType":"basic","points":1,"front":"When reflecting a point in the $y$-axis, how do the coordinates change?","back":"The $x$-coordinate changes sign (multiplied by -1).","mcqOptions":[{"text":"The $x$-coordinate changes sign (multiplied by -1).","correct":true,"explanation":"Reflection in the $y$-axis reverses a point’s horizontal position, so the $x$-coordinate changes sign while the $y$-coordinate remains unchanged."},{"text":"The $y$-coordinate changes sign (multiplied by -1).","correct":false,"explanation":"Changing the $y$-coordinate reflects a point in the $x$-axis. Reflection in the $y$-axis instead changes the sign of the $x$-coordinate."},{"text":"The $x$- and $y$-coordinates change sign (multiplied by -1).","correct":false,"explanation":"Changing both coordinate signs produces a rotation of $180°$ about the origin. Reflection in the $y$-axis changes only the $x$-coordinate’s sign."},{"text":"The $x$-coordinate stays unchanged (multiplied by 1).","correct":false,"explanation":"Leaving the $x$-coordinate unchanged would not reverse the point’s horizontal position. Reflection in the $y$-axis changes the sign of the $x$-coordinate."}]},{"id":"f68a7b6a-0d19-2efe-88b4-b846973862f6","cardType":"basic","points":1,"front":"What is the coordinate rule for a reflection in the line $y=x$?","back":"$$(x, y) \\to (y, x)$ (swap the coordinates).","mcqOptions":[{"text":"$$(x, y) \\to (y, x)$ (swap the coordinates).","correct":true,"explanation":"The line $y=x$ treats the horizontal and vertical directions symmetrically, so reflection in this line swaps the $x$- and $y$-coordinates."},{"text":"$$(x, y) \\to (-x, y)$ (change the sign of $x$).","correct":false,"explanation":"Changing only the sign of $x$ is the rule for reflection in the $y$-axis. Reflection in $y=x$ swaps the two coordinates."},{"text":"$$(x, y) \\to (x, -y)$ (change the sign of $y$).","correct":false,"explanation":"Changing only the sign of $y$ is the rule for reflection in the $x$-axis. Reflection in $y=x$ instead swaps the coordinates."},{"text":"$$(x, y) \\to (-y, -x)$ (swap and change the signs).","correct":false,"explanation":"Swapping both coordinates and changing their signs reflects a point in $y=-x$. Reflection in $y=x$ swaps the coordinates without changing their signs."}]},{"id":"184fd6b9-f356-e6e3-342d-56492e33cced","cardType":"cloze","points":null,"front":"In a reflection, corresponding vertices are the [ ] from the mirror line, on opposite sides.","back":"In a reflection, corresponding vertices are the same distance from the mirror line, on opposite sides.","mcqOptions":[{"text":"same distance","correct":true,"explanation":"A reflection places each image vertex the same perpendicular distance from the mirror line as its corresponding object vertex, preserving symmetry across the line."},{"text":"double distance","correct":false,"explanation":"Doubling the distance describes a change in size rather than a reflection. Corresponding vertices must be the same perpendicular distance from the mirror line."},{"text":"half distance","correct":false,"explanation":"Halving the distance would move the image closer to the mirror line and break reflection symmetry. The two corresponding vertices must be the same distance away."},{"text":"different distances","correct":false,"explanation":"Unequal distances from the mirror line do not produce corresponding reflected points. Each object vertex and its image must be the same perpendicular distance from the line."}]},{"id":"e6240e5a-1f09-a49a-ce8c-7ede29abd804","cardType":"cloze","points":null,"front":"In a reflection, corresponding vertices are the same distance from the mirror line, on [ ].","back":"In a reflection, corresponding vertices are the same distance from the mirror line, on opposite sides.","mcqOptions":[{"text":"opposite sides","correct":true,"explanation":"The mirror line lies between each object vertex and its corresponding image vertex, so the two points are equally distant from it on opposite sides."},{"text":"the same side","correct":false,"explanation":"Placing both vertices on the same side does not create a reflection across the line. Corresponding vertices must lie on opposite sides of the mirror line."},{"text":"one side only","correct":false,"explanation":"A reflection crosses the mirror line rather than keeping both corresponding vertices on one side. They must be equally distant on opposite sides of the line."},{"text":"either side at random","correct":false,"explanation":"The side is not chosen randomly in a reflection. Each image vertex must be positioned on the opposite side of the mirror line from its object vertex."}]},{"id":"b35b626d-71a9-cafa-3a22-38bf0f280a9e","cardType":"basic","points":3,"front":"What three details are required to describe a rotation fully?","back":"

Angle (e.g. $90^{\\circ}$)
Direction (clockwise or anticlockwise)
Centre of rotation

","mcqOptions":[{"text":"

Angle (e.g. $90^{\\circ}$)
Direction (clockwise or anticlockwise)
Centre of rotation

","correct":true,"explanation":"A rotation is uniquely determined by how far it turns, which way it turns, and the fixed point about which the turn is made."},{"text":"

Angle (e.g. $90^{\\circ}$)
Direction (clockwise or anticlockwise)
Mirror line

","correct":false,"explanation":"A mirror line belongs to a reflection, not a rotation. A rotation requires an angle, a clockwise or anticlockwise direction, and a centre of rotation."},{"text":"

Angle (e.g. $90^{\\circ}$)
Scale factor
Centre of rotation

","correct":false,"explanation":"Scale factor describes an enlargement and does not specify which way a shape turns. The missing detail is the clockwise or anticlockwise direction."},{"text":"

Direction (clockwise or anticlockwise)
Centre of rotation
Translation vector

","correct":false,"explanation":"A translation vector describes movement without turning and cannot replace the rotation angle. The required details are angle, direction, and centre of rotation."}]},{"id":"8768df1a-79df-ae92-0eb3-50625a6a1f40","cardType":"basic","points":1,"front":"What is the coordinate rule for a $180^{\\circ}$ rotation about the origin?","back":"$$(x, y) \\to (-x, -y)$.","mcqOptions":[{"text":"$$(x, y) \\to (-x, -y)$.","correct":true,"explanation":"A $180^{\\circ}$ rotation sends each point to the position directly opposite through the origin, so both the $x$-coordinate and $y$-coordinate change sign."},{"text":"$$(x, y) \\to (-y, x)$.","correct":false,"explanation":"Swapping the coordinates and negating the original $y$-coordinate gives a $90^{\\circ}$ anticlockwise rotation. For $180^{\\circ}$, both coordinates simply change sign."},{"text":"$$(x, y) \\to (y, -x)$.","correct":false,"explanation":"This rule represents a $90^{\\circ}$ clockwise rotation about the origin. A $180^{\\circ}$ rotation instead maps the point to $(-x,-y)$."},{"text":"$$(x, y) \\to (-x, y)$.","correct":false,"explanation":"Changing only the sign of $x$ reflects a point in the $y$-axis. A $180^{\\circ}$ rotation changes the signs of both coordinates."}]},{"id":"e85f63db-4805-7861-e7a5-ef56896dccc4","cardType":"basic","points":1,"front":"What is the coordinate rule for a $90^{\\circ}$ anticlockwise rotation about the origin?","back":"$$(x, y) \\to (-y, x)$.","mcqOptions":[{"text":"$$(x, y) \\to (-y, x)$.","correct":true,"explanation":"For a $90^{\\circ}$ anticlockwise rotation about the origin, the coordinates swap positions and the original $y$-coordinate becomes negative."},{"text":"$$(x, y) \\to (y, -x)$.","correct":false,"explanation":"This coordinate rule turns points $90^{\\circ}$ clockwise, reversing the required direction. Anticlockwise rotation uses $(-y,x)$ instead."},{"text":"$$(x, y) \\to (-x, -y)$.","correct":false,"explanation":"Negating both coordinates sends a point to the opposite side of the origin, which is a $180^{\\circ}$ rotation rather than a $90^{\\circ}$ anticlockwise rotation."},{"text":"$$(x, y) \\to (-x, y)$.","correct":false,"explanation":"Negating only the $x$-coordinate reflects the point in the $y$-axis. A $90^{\\circ}$ anticlockwise rotation swaps the coordinates and gives $(-y,x)$."}]},{"id":"9a7c9727-b163-3221-b04d-9bb61fbff14b","cardType":"basic","points":2,"front":"What two details are required to describe an enlargement fully?","back":"

Scale factor
Centre of enlargement

","mcqOptions":[{"text":"

Scale factor
Centre of enlargement

","correct":true,"explanation":"The scale factor determines the change in size, while the centre of enlargement determines the point from which corresponding vertices are projected."},{"text":"

Scale factor
Direction

","correct":false,"explanation":"Clockwise or anticlockwise direction is needed for a rotation, not an enlargement. An enlargement is fully described by its scale factor and centre of enlargement."},{"text":"

Scale factor
Angle

","correct":false,"explanation":"An angle describes the amount of turning in a rotation and does not locate an enlargement. The second required detail is the centre of enlargement."},{"text":"

Centre of enlargement
Translation vector

","correct":false,"explanation":"A translation vector describes a fixed movement and gives no change in size. An enlargement requires its centre of enlargement and its scale factor."}]},{"id":"4540f719-eb75-70ce-8c95-b23f5cc2cda1","cardType":"cloze","points":null,"front":"For an enlargement with scale factor $k$ and centre $O$, the coordinates of the image are found by [ ] the object coordinates by $k$.","back":"For an enlargement with scale factor $k$ and centre $O$, the coordinates of the image are found by multiplying the object coordinates by $k$.","mcqOptions":[{"text":"multiplying","correct":true,"explanation":"With the centre at the origin $O$, multiplying each coordinate by $k$ scales its distance and direction from the origin by the required scale factor."},{"text":"dividing","correct":false,"explanation":"Dividing by $k$ applies the reciprocal scale factor $\\frac{1}{k}$ rather than $k$. The object coordinates must be multiplied by $k$."},{"text":"adding","correct":false,"explanation":"Adding $k$ to coordinates produces a translation-like shift and does not scale distances proportionally. An enlargement about the origin is found by multiplying coordinates by $k$."},{"text":"subtracting","correct":false,"explanation":"Subtracting $k$ changes coordinates by a fixed amount instead of scaling their distances from the origin. The coordinates must be multiplied by $k$."}]},{"id":"b5f0c294-3a30-87a9-97cc-b031979abb84","cardType":"cloze","points":null,"front":"For an enlargement with scale factor $k$ and centre $O$, the coordinates of the image are found by multiplying the object coordinates by $\\text{[...]}$.","back":"For an enlargement with scale factor $k$ and centre $O$, the coordinates of the image are found by multiplying the object coordinates by $\\boxed{k}$.","mcqOptions":[{"text":"$$k$","correct":true,"explanation":"The scale factor $k$ multiplies each coordinate, so every point’s distance from the centre of enlargement is scaled by the same factor."},{"text":"$$k^2$","correct":false,"explanation":"Squaring the scale factor confuses length scale factor with area scale factor. Coordinates represent lengths, so they are multiplied by $k$, not $k^2$."},{"text":"$$\\frac{1}{k}$","correct":false,"explanation":"Using the reciprocal reverses the intended enlargement and applies scale factor $\\frac{1}{k}$. To perform an enlargement with scale factor $k$, multiply by $k$."},{"text":"$$-k$","correct":false,"explanation":"The negative sign would place image points on the opposite side of the centre as well as scaling them. The stated scale factor is $k$, so coordinates use $k$."}]},{"id":"8385e391-8164-2fc0-4df2-082b94e4df8d","cardType":"basic","points":1,"front":"Which transformation changes the size of a shape while keeping it the same proportions?","back":"An enlargement.","mcqOptions":[{"text":"An enlargement.","correct":true,"explanation":"An enlargement changes a shape’s dimensions by a scale factor while preserving its proportions, so the image remains mathematically similar to the original shape."},{"text":"A translation.","correct":false,"explanation":"A translation moves every point by the same vector without changing the shape’s size. An enlargement changes size while preserving the shape’s proportions."},{"text":"A reflection.","correct":false,"explanation":"A reflection flips a shape across a mirror line but leaves its dimensions unchanged. An enlargement is the transformation that changes size while preserving proportions."},{"text":"A rotation.","correct":false,"explanation":"A rotation turns a shape about a centre without altering its dimensions. An enlargement changes the dimensions by a scale factor while maintaining the same proportions."}]},{"id":"4b48ffa8-dc6e-3459-ae57-494903ab5cc0","cardType":"basic","points":1,"front":"Why is the order of combined transformations important?","back":"Performing transformations in a different order can result in a different final image.","mcqOptions":[{"text":"Performing transformations in a different order can result in a different final image.","correct":true,"explanation":"Many transformations are not commutative, meaning that reversing their order can move points to different positions and therefore produce a different final image."},{"text":"Performing transformations in a different order always results in the same final image.","correct":false,"explanation":"It is tempting to assume transformations commute, but many do not. Changing their order can move points to different positions and produce a different final image."},{"text":"Performing transformations in a different order only changes the names of the vertices.","correct":false,"explanation":"The order can affect the actual positions of the transformed vertices, not merely their labels. A different order can therefore produce a different final image."},{"text":"Performing transformations in a different order only changes the description of the method.","correct":false,"explanation":"Reordering transformations does more than alter how the method is described. Because many transformations do not commute, it can produce a different final image."}]},{"id":"5ea89000-5b01-88e1-e295-285e11905185","cardType":"basic","points":1,"front":"What is the equation for the mirror line if it is the $y$-axis?","back":"$$x = 0$.","mcqOptions":[{"text":"$$x = 0$.","correct":true,"explanation":"Every point on the $y$-axis has an $x$-coordinate of zero, so the equation of this vertical mirror line is $x = 0$."},{"text":"$$y = 0$.","correct":false,"explanation":"This is the equation of the $x$-axis, a common axis-label reversal. Every point on the $y$-axis instead satisfies $x = 0$."},{"text":"$$x = 1$.","correct":false,"explanation":"This describes a vertical line one unit to the right of the $y$-axis. The $y$-axis passes through points whose $x$-coordinate is zero, so its equation is $x = 0$."},{"text":"$$y = x$.","correct":false,"explanation":"This describes a diagonal line through the origin, not the vertical $y$-axis. The equation of the $y$-axis is $x = 0$."}]},{"id":"1f4e785c-59ab-6812-552b-41c97cbe2d63","cardType":"cloze","points":null,"front":"The point where the $x$-axis and $y$-axis intersect is called the [ ] and has coordinates $(0,0)$.","back":"The point where the $x$-axis and $y$-axis intersect is called the origin and has coordinates $(0,0)$.","mcqOptions":[{"text":"origin","correct":true,"explanation":"The origin is the unique point where the two coordinate axes intersect. Its $x$-coordinate and $y$-coordinate are both zero, giving $(0,0)$."},{"text":"midpoint","correct":false,"explanation":"A midpoint is halfway between two specified points, so it does not necessarily lie where the axes meet. Their intersection at $(0,0)$ is called the origin."},{"text":"intercept","correct":false,"explanation":"An intercept is where a graph crosses an axis, rather than the name of the axes’ intersection. The $x$-axis and $y$-axis meet at the origin."},{"text":"centre","correct":false,"explanation":"Although the axes may appear centred on a coordinate grid, their intersection has the specific mathematical name origin and has coordinates $(0,0)$."}]},{"id":"d8658ac1-448e-8ddf-d94b-4b4e5033f625","cardType":"cloze","points":null,"front":"The point where the $x$-axis and $y$-axis intersect is called the origin and has coordinates $\\text{[...]}$.","back":"The point where the $x$-axis and $y$-axis intersect is called the origin and has coordinates $\\boxed{(0,0)}$.","mcqOptions":[{"text":"$$(0,0)$","correct":true,"explanation":"At the origin, the point is neither horizontally nor vertically displaced from the axes’ intersection. Therefore both coordinates are zero, giving $(0,0)$."},{"text":"$$(0,1)$","correct":false,"explanation":"This point lies on the $y$-axis one unit above the origin. The axes themselves intersect where both coordinates are zero, at $(0,0)$."},{"text":"$$(1,0)$","correct":false,"explanation":"This point lies on the $x$-axis one unit to the right of the origin. The intersection of both axes has coordinates $(0,0)$."},{"text":"$$(1,1)$","correct":false,"explanation":"This point is one unit right and one unit above the axes’ intersection. At the origin, both coordinates are zero, so the coordinates are $(0,0)$."}]},{"id":"f286bd72-c8b8-4ea7-a5b3-581edfcc9b3a","cardType":"basic","points":2,"front":"If a vertex moves from $(-2, -1)$ to $(4, 2)$, what is the translation vector?","back":"$$\\begin{pmatrix} 6 \\\\ 3 \\end{pmatrix}$.","mcqOptions":[{"text":"$$\\begin{pmatrix} 6 \\\\ 3 \\end{pmatrix}$.","correct":true,"explanation":"Subtract the starting coordinates from the final coordinates: $4-(-2)=6$ horizontally and $2-(-1)=3$ vertically, giving the translation vector $\\begin{pmatrix}6\\\\3\\end{pmatrix}$."},{"text":"$$\\begin{pmatrix} -6 \\\\ -3 \\end{pmatrix}$.","correct":false,"explanation":"This reverses the subtraction and gives the vector for moving from the final point back to the start. Final minus initial gives $\\begin{pmatrix}6\\\\3\\end{pmatrix}$."},{"text":"$$\\begin{pmatrix} 4 \\\\ 2 \\end{pmatrix}$.","correct":false,"explanation":"These are the destination coordinates, not the change in position. Subtracting the initial coordinates from them gives $4-(-2)=6$ and $2-(-1)=3$."},{"text":"$$\\begin{pmatrix} 2 \\\\ 1 \\end{pmatrix}$.","correct":false,"explanation":"This comes from adding the negative starting coordinates rather than subtracting them. Subtracting a negative gives $4-(-2)=6$ and $2-(-1)=3$."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Component 1"},"heading":"Transformations","title":"Transformations Flashcards","topbar":{"backHref":"/gcse/maths/eduqas/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"4759973e-3cee-4a25-86fc-9dbc0f1035b0","walled":"$L39"}],"$L3a","$L3b"]