Cambridge International AS Level · Mathematics (9709)

Coordinate geometry: Practice Questions

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

10 questions25 marksFree, no account

Question 1

1 mark

Determine the gradient of the straight line with the equation \(3x - 2y + 6 = 0\).

Question 2

1 mark

Find the equation of the line which passes through the point \((1, 2)\) and is perpendicular to the line with equation \(y = 2x + 5\).

Question 3

1 mark

Find the values of the constant \(k\) for which the line \(y = 2x + k\) is a tangent to the circle \(x^2 + y^2 = 5\).

Question 4

1 mark

Find the coordinates of the midpoint of the line segment joining the points A\((2, -3)\) and B\((6, 7)\).

Question 5

1 mark

Find the equation of the circle with centre \((3, -4)\) that passes through the point \((7, -1)\).

Question 6

3 marks

Find the gradient of a line that is perpendicular to the straight line passing through the points A \( (1, 4) \) and B \( (3, 10) \).

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

Question 7

4 marks

A circle has the equation \( (x - 2)^2 + (y + 3)^2 = 25 \). Find the coordinates of the two points where the circle intersects the \( x \)-axis.

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Question 8

5 marks

Point A has coordinates \( (1, 2) \) and point B has coordinates \( (5, 10) \). Find the equation of the perpendicular bisector of the line segment AB, giving your answer in the form \( ay + bx = c \).

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

Question 9

3 marks

A straight line passes through the points \( A(-2, 5) \) and \( B(4, 13) \).

(a) Find the equation of the line \( AB \), giving your answer in the form \( y = mx + c \).
(b) Find the length of the line segment \( AB \).

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

Question 10

5 marks

The circle \( C \) has the equation \( (x-3)^2 + (y+2)^2 = 25 \).

(a) Write down the coordinates of the centre of the circle and its radius.
(b) Find the equation of the tangent to the circle at the point \( (6, 2) \), giving your answer in the form \( ax + by + c = 0 \).

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

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