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Values of x increase to the right and decrease to the left."},{"text":"y-axis","correct":false,"explanation":"The y-axis is the vertical line, not the horizontal one. The horizontal line is the x-axis, showing movement left or right."},{"text":"origin","correct":false,"explanation":"The origin is the single point where the two axes intersect. The horizontal line through that point is the x-axis."},{"text":"line y = x","correct":false,"explanation":"The line $y = x$ is diagonal because both coordinates change together. The horizontal axis of a coordinate grid is the x-axis."}]},{"id":"f1c056d6-df54-0253-e914-22600111db1f","cardType":"basic","points":1,"front":"In a coordinate grid, which axis is the vertical line?","back":"y-axis","mcqOptions":[{"text":"y-axis","correct":true,"explanation":"The y-axis runs vertically through a coordinate grid. Values of y increase upwards and decrease downwards."},{"text":"x-axis","correct":false,"explanation":"The x-axis is the horizontal line, not the vertical one. The vertical line is the y-axis, showing movement up or down."},{"text":"origin","correct":false,"explanation":"The origin is a point where the x-axis and y-axis intersect, rather than an axis itself. The vertical line is the y-axis."},{"text":"line y = x","correct":false,"explanation":"The line $y = x$ slopes diagonally rather than running vertically. The y-axis is the vertical line on a coordinate grid."}]},{"id":"748ded60-17fe-8b61-df54-582b67400df7","cardType":"basic","points":1,"front":"What is the standard order for reading or writing a coordinate pair?","back":"Across (x) first, then up/down (y).","mcqOptions":[{"text":"Across (x) first, then up/down (y).","correct":true,"explanation":"A coordinate pair is written $(x,y)$, so the horizontal x-coordinate is read first and the vertical y-coordinate is read second."},{"text":"Up/down (y) first, then across (x).","correct":false,"explanation":"This reverses the standard coordinate order. Coordinates are written $(x,y)$, so move across using x first, then up or down using y."},{"text":"Across (y) first, then up/down (x).","correct":false,"explanation":"This swaps the meanings of x and y. The x-coordinate describes movement across, while the y-coordinate describes movement up or down."},{"text":"Up/down (x) first, then across (y).","correct":false,"explanation":"This assigns each direction to the wrong axis. Movement across is controlled by x and comes first; vertical movement is controlled by y."}]},{"id":"3f713fe8-d8c2-3a82-2423-590290669f58","cardType":"basic","points":1,"front":"What direction does a negative x-coordinate indicate?","back":"Move left from the origin.","mcqOptions":[{"text":"Move left from the origin.","correct":true,"explanation":"Negative x-values lie to the left of the origin because x-values decrease as you move left along the horizontal axis."},{"text":"Move right from the origin.","correct":false,"explanation":"Moving right produces a positive x-coordinate, not a negative one. A negative x-coordinate means moving left from the origin."},{"text":"Move up from the origin.","correct":false,"explanation":"Moving up changes the y-coordinate rather than the x-coordinate. A negative x-coordinate requires horizontal movement to the left from the origin."},{"text":"Move down from the origin.","correct":false,"explanation":"Moving down represents a negative y-coordinate, not a negative x-coordinate. Negative x-values are reached by moving left from the origin."}]},{"id":"4775d23e-989d-3898-63bb-91f403363534","cardType":"basic","points":1,"front":"What direction does a negative y-coordinate indicate?","back":"Move down from the x-axis.","mcqOptions":[{"text":"Move down from the x-axis.","correct":true,"explanation":"Negative y-values lie below the x-axis because y-values decrease as you move downwards on a coordinate grid."},{"text":"Move up from the x-axis.","correct":false,"explanation":"Moving up from the x-axis produces a positive y-coordinate. A negative y-coordinate is found by moving down from the x-axis."},{"text":"Move left from the y-axis.","correct":false,"explanation":"Moving left changes the x-coordinate rather than the y-coordinate. A negative y-coordinate requires downward movement from the x-axis."},{"text":"Move right from the y-axis.","correct":false,"explanation":"Moving right changes the x-coordinate and usually represents a positive x-value. Negative y-values are reached by moving down from the x-axis."}]},{"id":"4f5989da-ca38-6cee-bb26-da679fb03e54","cardType":"cloze","points":null,"front":"To plot the point $(-1, 3)$, you start at the origin and move [ ] and then 3 squares up.","back":"To plot the point $(-1, 3)$, you start at the origin and move 1 square left and then 3 squares up.","mcqOptions":[{"text":"1 square left","correct":true,"explanation":"The first coordinate is $-1$, so move one square in the negative x-direction, which is left, before using the y-coordinate."},{"text":"1 square right","correct":false,"explanation":"Moving right treats $-1$ as positive. The negative first coordinate means moving 1 square left before moving 3 squares up."},{"text":"3 squares left","correct":false,"explanation":"This incorrectly uses the y-coordinate, 3, for the horizontal movement. The x-coordinate is $-1$, so the correct move is 1 square left."},{"text":"1 square down","correct":false,"explanation":"Moving down changes the y-coordinate rather than the x-coordinate. The first coordinate $-1$ requires a move of 1 square left."}]},{"id":"947c9367-7f35-4058-9d5a-95cca888a764","cardType":"cloze","points":null,"front":"To plot the point $(-1, 3)$, you start at the origin and move 1 square left and then [ ].","back":"To plot the point $(-1, 3)$, you start at the origin and move 1 square left and then 3 squares up.","mcqOptions":[{"text":"3 squares up","correct":true,"explanation":"The second coordinate is positive 3, so after the horizontal movement you move three squares upwards in the positive y-direction."},{"text":"3 squares down","correct":false,"explanation":"Moving down would represent a y-coordinate of $-3$. Since the second coordinate is positive 3, the correct movement is 3 squares up."},{"text":"1 square up","correct":false,"explanation":"This mistakenly reuses the magnitude of the x-coordinate. The y-coordinate is 3, so the vertical movement must be 3 squares up."},{"text":"3 squares right","correct":false,"explanation":"Moving right changes the x-coordinate instead of the y-coordinate. The second coordinate is positive 3, requiring a vertical move of 3 squares up."}]},{"id":"b5d86cb6-79b5-3f85-2d4b-584652845a35","cardType":"basic","points":1,"front":"What is the midpoint of a line segment?","back":"The point exactly halfway between two endpoints.","mcqOptions":[{"text":"The point exactly halfway between two endpoints.","correct":true,"explanation":"A midpoint divides a line segment into two equal lengths, so it is exactly halfway between the segment’s two endpoints."},{"text":"The point one quarter of the way between two endpoints.","correct":false,"explanation":"A point one quarter of the way does not divide the segment equally. The midpoint is exactly halfway between the two endpoints."},{"text":"The point where the segment crosses the x-axis.","correct":false,"explanation":"Crossing the x-axis is unrelated to being a midpoint and may not occur at all. The midpoint is exactly halfway between the endpoints."},{"text":"The point at either end of the line segment.","correct":false,"explanation":"An endpoint marks a boundary of the segment rather than its centre. The midpoint lies exactly halfway between the two endpoints."}]},{"id":"e0f285cd-9319-1897-aacb-0c2b64baa3cd","cardType":"basic","points":2,"front":"How do you calculate the midpoint of two coordinates?","back":"

Average the x-coordinates.
Average the y-coordinates.

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

Average the x-coordinates.
Average the y-coordinates.

","correct":true,"explanation":"The midpoint lies halfway between the points in both directions, so calculate the mean of the two x-coordinates and separately calculate the mean of the two y-coordinates."},{"text":"

Add the x-coordinates.
Add the y-coordinates.

","correct":false,"explanation":"Adding gives the coordinate totals but omits division by 2. The midpoint is found by averaging each pair, so add the x-coordinates and divide by 2, then repeat for y."},{"text":"

Subtract the x-coordinates.
Subtract the y-coordinates.

","correct":false,"explanation":"Subtracting coordinates finds the change between the points, not their midpoint. Average the x-coordinates and average the y-coordinates to locate the point halfway between them."},{"text":"

Average the x-coordinates.
Add the y-coordinates.

","correct":false,"explanation":"Only the x-coordinate has been averaged here. Both components must be treated alike: average the x-coordinates and also average the y-coordinates to obtain the midpoint."}]},{"id":"c9b6c0a8-55f9-d8ad-b53e-ece5ab3324ec","cardType":"cloze","points":null,"front":"To find the middle of two coordinates, you [ ] the values together and divide by 2.","back":"To find the middle of two coordinates, you add the values together and divide by 2.","mcqOptions":[{"text":"add","correct":true,"explanation":"The mean of two coordinate values is their sum divided by 2. Therefore, the first step in finding the middle value is to add the two values."},{"text":"subtract","correct":false,"explanation":"Subtracting finds the difference or displacement between two coordinate values, not their middle. To find the midpoint, add the values together and then divide the result by 2."},{"text":"multiply","correct":false,"explanation":"Multiplying the coordinate values does not calculate their mean. The midpoint coordinate is found by adding the two corresponding values and dividing their sum by 2."},{"text":"square","correct":false,"explanation":"Squaring is used in calculations such as distances, but it does not find a middle coordinate. Add the corresponding coordinate values together before dividing by 2."}]},{"id":"ce131dde-a4b4-39a2-e736-b39f91c93c5d","cardType":"cloze","points":null,"front":"To find the middle of two coordinates, you add the values together and [ ].","back":"To find the middle of two coordinates, you add the values together and divide by 2.","mcqOptions":[{"text":"divide by 2","correct":true,"explanation":"There are two coordinate values being averaged, so their sum must be divided by 2. This gives the coordinate exactly halfway between the original values."},{"text":"multiply by 2","correct":false,"explanation":"Multiplying the sum by 2 makes it larger rather than finding its mean. Because two values are being averaged, their sum must be divided by 2."},{"text":"divide by 4","correct":false,"explanation":"Dividing by 4 would be appropriate when averaging four values, not two. A midpoint uses two corresponding coordinates, so their sum is divided by 2."},{"text":"subtract 2","correct":false,"explanation":"Subtracting 2 is not the same as calculating an average and produces no consistent midpoint. Add the two corresponding coordinate values, then divide their sum by 2."}]},{"id":"cfa1fd80-758a-10d1-b5e8-197f7ba5ebc5","cardType":"basic","points":2,"front":"Calculate the midpoint of $B(-3, 3)$ and $C(3, 0)$.","back":"$$(0, 1.5)$","mcqOptions":[{"text":"$$(0, 1.5)$","correct":true,"explanation":"Averaging the x-coordinates gives $(-3+3)/2=0$, while averaging the y-coordinates gives $(3+0)/2=1.5$. Therefore, the midpoint is $(0, 1.5)$."},{"text":"$$(0, 3)$","correct":false,"explanation":"The x-coordinate has been averaged correctly, but the y-values were only added. Dividing their sum by 2 gives $(3+0)/2=1.5$, so the midpoint is $(0, 1.5)$."},{"text":"$$(3, 1.5)$","correct":false,"explanation":"Treating $-3$ as $3$ loses its negative sign and gives the wrong x-coordinate. The correct average is $(-3+3)/2=0$, so the midpoint is $(0, 1.5)$."},{"text":"$$(0, -1.5)$","correct":false,"explanation":"The negative y-value results from subtracting the y-coordinates instead of adding them. Their average is $(3+0)/2=1.5$, giving the midpoint $(0, 1.5)$."}]},{"id":"b1e64008-fee3-642a-d9d9-feed46eb2e76","cardType":"basic","points":1,"front":"What is the orientation of a line with an equation like $x = 3$?","back":"Vertical","mcqOptions":[{"text":"Vertical","correct":true,"explanation":"The equation fixes the x-coordinate at 3 while the y-coordinate can take any value. The resulting points form a vertical line through $x=3$."},{"text":"Horizontal","correct":false,"explanation":"This confuses equations of the forms $x=a$ and $y=b$. A fixed x-coordinate produces a vertical line; a fixed y-coordinate produces a horizontal line."},{"text":"Diagonal","correct":false,"explanation":"A diagonal line requires both coordinates to vary according to a relationship. In $x=3$, the x-coordinate remains fixed, so the line is vertical."},{"text":"Curved","correct":false,"explanation":"An equation fixing one coordinate at a constant produces a straight line, not a curve. Since $x$ is always 3, the line is vertical."}]},{"id":"e3288750-7731-16d8-1337-91a9147d5ef2","cardType":"basic","points":1,"front":"What is the orientation of a line with an equation like $y = 6$?","back":"Horizontal","mcqOptions":[{"text":"Horizontal","correct":true,"explanation":"The equation fixes the y-coordinate at 6 while the x-coordinate can take any value. These points form a horizontal line through $y=6$."},{"text":"Vertical","correct":false,"explanation":"This reverses the roles of x and y. A fixed y-coordinate produces a horizontal line, whereas a fixed x-coordinate produces a vertical line."},{"text":"Diagonal","correct":false,"explanation":"A diagonal line requires the y-coordinate to change as the x-coordinate changes. Here y remains fixed at 6, so the line is horizontal."},{"text":"Curved","correct":false,"explanation":"A constant y-coordinate creates a straight line rather than a curve. Because every point has $y=6$, the line runs horizontally across the coordinate grid."}]},{"id":"9758fe78-a87c-adb3-fc4f-ad09240b4f07","cardType":"cloze","points":null,"front":"Every point on the line $y = 4$ has a [ ] of 4.","back":"Every point on the line $y = 4$ has a y-coordinate of 4.","mcqOptions":[{"text":"y-coordinate","correct":true,"explanation":"In an equation of the form $y=a$, every point has the same y-coordinate, $a$. Therefore, all points on $y=4$ have a y-coordinate of 4."},{"text":"x-coordinate","correct":false,"explanation":"The x-coordinate is free to vary along this line, so it is not always 4. The equation fixes the y-coordinate at 4, creating a horizontal line."},{"text":"gradient","correct":false,"explanation":"A horizontal line has gradient 0, not 4. The number 4 in $y=4$ specifies the y-coordinate shared by every point on the line."},{"text":"distance from y-axis","correct":false,"explanation":"Distance from the y-axis depends on the magnitude of the x-coordinate, which varies along the line. It is the y-coordinate that remains fixed at 4."}]},{"id":"dac9d5f8-08d5-dda1-8f10-b6227cb194ab","cardType":"cloze","points":null,"front":"Every point on the line $y = 4$ has a y-coordinate of [ ].","back":"Every point on the line $y = 4$ has a y-coordinate of 4.","mcqOptions":[{"text":"4","correct":true,"explanation":"The equation $y=4$ directly states that the y-coordinate of every point is 4. The x-coordinate may vary, producing a horizontal line."},{"text":"0","correct":false,"explanation":"A y-coordinate of 0 would place points on the x-axis, whose equation is $y=0$. On the given line, every y-coordinate is 4."},{"text":"-4","correct":false,"explanation":"The negative sign would describe the different horizontal line $y=-4$, below the x-axis. The stated equation fixes every y-coordinate at positive 4."},{"text":"8","correct":false,"explanation":"Doubling the constant changes the line to $y=8$ and is not part of interpreting the equation. Every point on $y=4$ has y-coordinate 4."}]},{"id":"b8820045-bbfb-3e7c-03b8-76c3a6aa0789","cardType":"basic","points":2,"front":"How do you draw the line $x = -2$?","back":"Draw a vertical line through -2 on the x-axis.","mcqOptions":[{"text":"Draw a vertical line through -2 on the x-axis.","correct":true,"explanation":"An equation of the form $x = a$ fixes the x-coordinate while the y-coordinate can vary, producing a vertical line through $a$ on the x-axis."},{"text":"Draw a vertical line through 2 on the x-axis.","correct":false,"explanation":"Using $2$ loses the negative sign and gives the line $x = 2$. The required line is vertical and crosses the x-axis at $-2$."},{"text":"Draw a horizontal line through -2 on the y-axis.","correct":false,"explanation":"A horizontal line represents a constant y-coordinate, not a constant x-coordinate. Since $x$ is fixed at $-2$, draw a vertical line through $-2$ on the x-axis."},{"text":"Draw a horizontal line through 2 on the y-axis.","correct":false,"explanation":"This confuses $x = -2$ with $y = 2$ and also loses the negative sign. The correct graph is vertical through $-2$ on the x-axis."}]},{"id":"dbd98569-2705-7ea1-8d33-4606251518b1","cardType":"basic","points":2,"front":"How do you draw the line $y = 4$?","back":"Draw a horizontal line through 4 on the y-axis.","mcqOptions":[{"text":"Draw a horizontal line through 4 on the y-axis.","correct":true,"explanation":"An equation of the form $y = a$ fixes the y-coordinate while the x-coordinate can vary, producing a horizontal line through $a$ on the y-axis."},{"text":"Draw a vertical line through 4 on the x-axis.","correct":false,"explanation":"A vertical line represents a constant x-coordinate, so this would draw $x = 4$. For $y = 4$, draw a horizontal line through $4$ on the y-axis."},{"text":"Draw a horizontal line through -4 on the y-axis.","correct":false,"explanation":"The negative sign changes the line to $y = -4$. The required line has y-coordinate $4$, so it is horizontal and crosses the y-axis at $4$."},{"text":"Draw a vertical line through -4 on the x-axis.","correct":false,"explanation":"This both treats the equation as $x = -4$ and changes the sign. The correct graph is a horizontal line through $4$ on the y-axis."}]},{"id":"7f9e8ccb-05d5-3432-aaa8-43757544475c","cardType":"basic","points":2,"front":"In a square $ABCD$, if the move from $B$ to $C$ is 1 left and 4 down, how do you find corner $D$?","back":"Move 1 left and 4 down starting from point A.","mcqOptions":[{"text":"Move 1 left and 4 down starting from point A.","correct":true,"explanation":"Opposite sides of a square are equal and parallel, so the movement from $A$ to $D$ matches the movement from $B$ to $C$: 1 left and 4 down."},{"text":"Move 1 left and 4 down starting from point B.","correct":false,"explanation":"Starting from $B$ and repeating the movement locates $C$, not $D$. To find $D$, apply the same movement of 1 left and 4 down from point $A$."},{"text":"Move 1 right and 4 down starting from point A.","correct":false,"explanation":"This reverses the horizontal direction and therefore does not make $AD$ equal and parallel to $BC$. From $A$, move 1 left and 4 down."},{"text":"Move 1 left and 4 up starting from point A.","correct":false,"explanation":"This reverses the vertical direction, using an upward movement instead of copying the vector from $B$ to $C$. From $A$, move 1 left and 4 down."}]},{"id":"f3be082d-93bf-5570-17b7-1713707f7186","cardType":"basic","points":2,"front":"What is the midpoint of $(4, -2)$ and $(4, 6)$?","back":"$$(4, 2)$","mcqOptions":[{"text":"$$(4, 2)$","correct":true,"explanation":"Average the coordinates separately: the x-coordinate remains $(4+4)/2=4$, while the y-coordinate is $(-2+6)/2=2$. Therefore the midpoint is $(4,2)$."},{"text":"$$(4, 4)$","correct":false,"explanation":"The value $4$ comes from adding the y-coordinates without dividing by $2$. Their mean is $(-2+6)/2=2$, while the mean x-coordinate is $4$."},{"text":"$$(0, 2)$","correct":false,"explanation":"This treats the common x-coordinate as though opposite values cancel. Both x-coordinates are $4$, so their mean is $4$; the mean y-coordinate is $2$."},{"text":"$$(8, 4)$","correct":false,"explanation":"This adds each pair of coordinates but does not divide by $2$. A midpoint uses coordinate averages, giving $((4+4)/2,(-2+6)/2)=(4,2)$."}]},{"id":"3326318e-558a-5e34-d509-d1e41f2966d9","cardType":"cloze","points":null,"front":"A [ ] is a straight line between two endpoints.","back":"A line segment is a straight line between two endpoints.","mcqOptions":[{"text":"line segment","correct":true,"explanation":"A line segment is the finite part of a line bounded by two endpoints. This distinguishes it from a line, which continues indefinitely in both directions."},{"text":"ray","correct":false,"explanation":"A ray has exactly one endpoint and continues indefinitely in one direction. A finite straight path bounded by two endpoints is called a line segment."},{"text":"line","correct":false,"explanation":"A line extends indefinitely in both directions and therefore has no endpoints. The part bounded by two endpoints is specifically called a line segment."},{"text":"perpendicular bisector","correct":false,"explanation":"A perpendicular bisector crosses a segment at its midpoint at a right angle; it is not the finite straight path between two endpoints. That path is a line segment."}]},{"id":"204f077c-89b9-93f8-5675-4c598e3f914c","cardType":"basic","points":1,"front":"If point A is 4 squares right and 2 squares below the origin, what are its coordinates?","back":"$$(4, -2)$","mcqOptions":[{"text":"$$(4, -2)$","correct":true,"explanation":"Moving 4 squares right makes the x-coordinate positive $4$, while moving 2 squares below the origin makes the y-coordinate negative $-2$."},{"text":"$$(4, 2)$","correct":false,"explanation":"This makes the vertical coordinate positive, as if the point were above the origin. Moving below the origin gives a negative y-coordinate, so the coordinates are $(4,-2)$."},{"text":"$$(-4, -2)$","correct":false,"explanation":"This makes the horizontal coordinate negative, as if the point were left of the origin. Moving right gives positive $4$, so the coordinates are $(4,-2)$."},{"text":"$$(-2, 4)$","correct":false,"explanation":"This swaps the horizontal and vertical movements. Coordinates are written as $(x,y)$, so 4 right gives $x=4$ and 2 below gives $y=-2$."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Component 1"},"heading":"Coordinates","title":"Coordinates Flashcards","topbar":{"backHref":"/gcse/maths/eduqas/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"44ae47a2-7410-42a4-b10c-f2c0aad5b6e6","walled":"$L39"}],"$L3a","$L3b"]