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1.5 Coordinate Geometry

1.5 Coordinate Geometry

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Question 98

The path of a robotic arm in a two-dimensional manufacturing grid (X,Y)(X, Y)(X,Y) is defined by the parametric equations

X=2p−51−4p,Y=121−4p,p≠14 X = \frac{2p - 5}{1 - 4p}, \quad Y = \frac{12}{1 - 4p}, \quad p \neq \frac{1}{4} X=1−4p2p−5​,Y=1−4p12​,p=41​

where p p\,p is a control parameter.

a.

Show that the robotic arm moves along a straight line.

[4]
b.

The arm's path intersects a safety perimeter defined by the line Y=3X+10Y = 3X + 10Y=3X+10. Determine the XXX-coordinate of this point of intersection.

[3]
Markscheme

1.5 Coordinate Geometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Coordinate Geometry

178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.

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