Cambridge International A 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

A line passes through the points \(A(2, -1)\) and \(B(8, 7)\). Find the coordinates of the midpoint of the line segment \(AB\).

Question 2

1 mark

Points \(A\) and \(B\) have coordinates \((1, 4)\) and \((5, 2)\) respectively. Find the equation of the perpendicular bisector of \(AB\).<\/p>

Question 3

1 mark

A circle passes through the points \((0, 0)\), \((8, 0)\) and \((0, 6)\). Find the equation of the circle.

Question 4

1 mark

Find the coordinates of the midpoint of the line segment joining the points \(P(-4, 7)\) and \(Q(2, -3)\).<\/p>

Question 5

1 mark

The equation of a circle is given by \(x^2 + y^2 - 4x + 6y - 3 = 0\). Find the radius of the circle.

Question 6

2 marks

A line segment has endpoints at \(A(1, 4)\) and \(B(7, 10)\). Calculate the coordinates of the midpoint of the line segment \(AB\).

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Question 7

5 marks

The line \(y = kx - 5\) is a tangent to the curve \(y = x^2 - 4x - 1\). Find the possible values of the constant \(k\).

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Question 8

6 marks

The line with equation \(3x - 4y + 12 = 0\) intersects the \(x\)-axis at point \(A\) and the \(y\)-axis at point \(B\). Find the equation of the perpendicular bisector of the line segment \(AB\).

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Question 9

3 marks

The points \(P\) and \(Q\) have coordinates \((1, -2)\) and \((7, 6)\) respectively.
(a) Calculate the length of the line segment \(PQ\).
(b) Find the coordinates of the midpoint of \(PQ\).

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Question 10

4 marks

The line \(y = x + k\) is a tangent to the curve \(y = x^2 - 5x + 12\).
(a) Show that the \(x\)-coordinate of the point of contact satisfies the equation \(x^2 - 6x + (12 - k) = 0\).
(b) Using the discriminant, find the value of the constant \(k\).

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

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