A-level · Coordinate geometry

Parallel and perpendicular linesExam-style questions

Parallel lines share a gradient; perpendicular gradients multiply to −1 (the negative reciprocal). Using both — and the perpendicular bisector of a segment — to find equations of lines.

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5 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

1
The points $A(1, 5)$ and $B(7, 1)$ are given.
(a) Find an equation of the perpendicular bisector of $AB$ . (4 marks)
(b) The perpendicular bisector meets the coordinate axes at the points $P$ and $Q$ . Find the area of triangle $OPQ$ , where $O$ is the origin. (2 marks)
Level 3 · 6 marksTry it
2
A triangle has vertices $A(0, 1)$ , $B(6, 3)$ and $C(2, 5)$ . Show that the triangle is right-angled at $C$ .
Level 3 · 3 marksTry it
3
The points are $A(-2, 5)$ and $B(4, -1)$ . The perpendicular bisector of $AB$ crosses the $x$ -axis at $P$ . Find the coordinates of $P$ .
Level 3 · 4 marksTry it
4
The points are $A(1, 2)$ and $B(5, 8)$ .
(a) Find the coordinates of the midpoint of $AB$ . (1 mark)
(b) Find an equation of the perpendicular bisector of $AB$ . (5 marks)
Level 3 · 6 marksTry it
5
$P$ is the point $(-3, 7)$ and $Q$ is the point $(5, 1)$
(a) Find the coordinates of the midpoint of $PQ$

(1 mark)
(b) Find the equation of the perpendicular bisector of $PQ$

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

(4 marks)
Level 3 · 5 marksTry it