Perpendicular gradients and line equations

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 3 marks
Line $L$ has equation $y = 2x - 3$ .
(a) Write down the gradient of a line perpendicular to $L$ . (1)
(b) Find the equation of the line perpendicular to $L$ that passes through $(4, 1)$ . (2)
Question 2Non-calculator · 5 marks
A is $(0,0)$ and B is $(10,8)$ .
(a) Find the perpendicular bisector of AB. (3)
(b) Find where the perpendicular bisector meets the x-axis. (2)
Question 3Non-calculator · 5 marks
A triangle has vertices $A(1, 1)$ , $B(4, 3)$ and $C(2, 6)$ .
(a) Show that angle $ABC$ is a right angle. (3)
(b) Work out the area of triangle ABC. (2)

Answers and marks

(a) $-\frac{1}{2}$

(b) $y = -\frac{1}{2}x + 3$

(a) $y=-\frac{5}{4}x+\frac{41}{4}$

(b) $(41/5,0)$

(a) Gradients $\frac{2}{3}$ and $-\frac{3}{2}$ multiply to $-1$ .

(b) $6.5$ square units

Perpendicular gradients and line equations

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