A-level · Coordinate geometry

Straight linesExam-style questions

The gradient of a line as a constant rate of change, the three forms of a line's equation — y = mx + c, y − y₁ = m(x − x₁), and ax + by + c = 0 — and how to move between them.

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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
In this question you must show all stages of your working.

Solutions relying on calculator technology are not acceptable.

The points $P$ and $Q$ have coordinates $(-\sqrt{5},\ 2)$ and $(3\sqrt{5},\ 10)$ respectively.
(a) Show that the gradient of the line segment $PQ$ can be written as $p\sqrt{5}$ , where $p$ is a rational number to be found.

You must show each step of your working.

(2 marks)

The line $l$ is the perpendicular bisector of $PQ$ .
(b) Find an equation for $l$ , giving your answer in the form $y = mx + c$ , where $m$ and $c$ are constants.

(3 marks)
Level 3 · 5 marksTry it
2
Show that the points $A(-1, -4)$ , $B(2, 2)$ and $C(4, 6)$ are collinear (lie on the same straight line).
Level 3 · 3 marksTry it
3
The points are $A(1, 1)$ , $B(5, 3)$ and $C(2, 7)$ .
(a) Find an equation of the line $AB$ . (3 marks)
(b) Find the area of triangle $ABC$ . (4 marks)
Level 3 · 7 marksTry it