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3.2 Co-ordinate geometry in the (x, y) plane (A-level only)

3.2 Co-ordinate geometry in the (x, y) plane (A-level only)

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Question 48

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

3.2 Co-ordinate geometry in the (x, y) plane (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.2 Co-ordinate geometry in the (x, y) plane (A-level only)

75 exam-style questions on CCEA A Level Maths 3.2 Co-ordinate geometry in the (x, y) plane (A-level only), covering 3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only) and 3.2.2 Co-ordinate geometry in the (x, y) plane (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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