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Edexcel A-Level Mathematics AS P1.2 Coordinate Geometry in the X Y Plane Questions

This topic uses descendant evidence from straight-line and perpendicular-line questions: calculate gradients, build equations and keep exact coordinates or surds.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • Find straight-line equations from two points or a point and gradient in the required form.
  • Use algebraic intersections to solve for exact x-values or coordinate pairs.
  • Apply perpendicular gradient rules when constructing related lines or locating points.

Covered syllabus points

P1.2.1 - Equation of a straight lineP1.2.2 - Parallel and perpendicular lines

Question 1

[Maximum number: 2]
Figure 2

Figure 2

Figure 2 shows a sketch of the straight line l and the curve C.
Given that l cuts the y-axis at -12 and cuts the x-axis at 4, as shown in Figure 2,

Given that C
- has equation y=f(x) where f(x) is a quadratic expression
- has a minimum point at (7,-18)
- cuts the x-axis at 4 and at k, where k is a constant

find an equation for l, writing your answer in the form y=mx+c, where m and c are constants to be found.

Question 2

[Maximum number: 3]
Figure 2

Figure 2

Figure 2 shows a sketch of
- the circle C with centre X(4,-3)
- the line l with equation y=52x−552y=\frac{5}{2} x-\frac{55}{2}

Given that l is the tangent to C at the point N,

show that an equation for the straight line passing through X and N is

2 x+5 y+7=0

Question 3

[Maximum number: 6]
Figure 2

Figure 2

Figure 2 shows the points P, Q and R.
Points P and Q have coordinates (-1,4) and (4,7) respectively.

Question (a)

(a)

Find an equation for the straight line passing through points P and Q.

Give your answer in the form ax+by+c=0 where a,b and c are integers.

[ 3 ]

Question (b)

(b)

The point R has coordinates (p,-3), where p is a positive constant.

Given that angle QPR=90∘QPR=90^\circ,

find the value of p.

(Solutions relying on calculator technology are not acceptable.)

[ 3 ]
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