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 straight line $l_1$ has equation

$3x + y - 7 = 0$

The point $A(-5,\ 2)$ lies on the line $l_2$ , which is perpendicular to $l_1$
(a) Find an equation for $l_2$

(2 marks)

The point $B$ is the point where $l_1$ and $l_2$ meet.
(b) Use algebra to find the coordinates of $B$ .

(3 marks)
(c) Hence find the shortest distance from $A$ to $l_1$ , giving your answer as a fully simplified surd.

(2 marks)
Level 4 · 7 marksTry it
2
The points $A$ and $B$ have coordinates $(-1, -4)$ and $(h, 5)$ respectively, where $h$ is a constant.
(a) Given that the gradient of $AB$ is $3$ , find the value of $h$ .

(2 marks)
(b) The line segment $AC$ has midpoint $B$ . Find the coordinates of $C$ .

(2 marks)
(c) The line through $A$ and $B$ meets the curve $y = x^2 - 7x + k$ , where $k$ is a constant, at two distinct points.

Determine the set of possible values of $k$ .

(6 marks)
Level 4 · 10 marksTry it