GCE O-Level · Mathematics (4052)

Coordinate geometry: Practice Questions

5 multiple-choice questions marked as you go, and 4 written questions with worked solutions. All on Coordinate geometry.

9 questions23 marksFree, no account

Question 1

1 mark

A line segment passes through the points \(A(2, 3)\) and \(B(5, 9)\). Calculate the gradient of the line segment \(AB\).

Question 2

1 mark

Find the equation of the straight line that passes through the points \( (2, 3) \) and \( (4, 7) \) in the form \( y = mx + c \).

Question 3

1 mark

The points \(P\) and \(Q\) have coordinates \((0, 4)\) and \((6, 0)\) respectively. Find the equation of the perpendicular bisector of the line segment \(PQ\).

Question 4

1 mark

Find the equation of the straight line that passes through the point \((1, 2)\) and has a gradient of \(-3\).

Question 5

1 mark

The point \( P(k, 4) \) lies on the line perpendicular to the line \( 2x + 3y = 6 \) and passing through the point \( (2, 1) \). Find the value of \( k \).

Question 6

2 marks

Find the gradient of the straight line that passes through the points \(A(2, 5)\) and \(B(-1, 14)\).

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Question 7

4 marks

The line \( L_1 \) passes through the points \( A(2, -3) \) and \( B(6, 5) \). Find the equation of the line \( L_2 \) which is the perpendicular bisector of the segment \( AB \).

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Question 8

5 marks

The points \( A \) and \( B \) have coordinates \( (-3, 2) \) and \( (5, 8) \) respectively.
(a) Find the length of the line segment \( AB \).
(b) Find the equation of the line \( L_1 \) which passes through \( A \) and \( B \).
(c) The line \( L_2 \) is perpendicular to \( L_1 \) and passes through the point \( (2, -1) \). Find the equation of \( L_2 \).
(d) Find the coordinates of the point where \( L_2 \) crosses the \( y \)-axis.

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Question 9

7 marks

The coordinates of three points are \( A(1, 2) \), \( B(5, 8) \) and \( C(9, 2) \).
(a) Find the equation of the line \( L \) that passes through \( B \) and is parallel to \( AC \).
(b) Find the equation of the perpendicular bisector of the line segment \( AB \).
(c) Find the coordinates of the point \( D \) where the perpendicular bisector of \( AB \) intersects the line \( L \).
(d) Calculate the area of the triangle \( ABC \).

Write your answer out first, then check it against the worked solution.

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