CIE iGCSE Maths E3.7 Perpendicular lines Exam Style Practice Questions- Paper 2

Question

Line L has equation $y = 4 – 5x$.

Find the equation of a line that is perpendicular to line L and passes through the point (0, 6).

▶️ Answer/Explanation

Solution

Ans: $y = \frac{1}{5}x + 6$

1. Original slope is -5, so perpendicular slope is $\frac{1}{5}$ (negative reciprocal)

2. Using point-slope form with point (0,6): $y – 6 = \frac{1}{5}(x – 0)$

3. Simplify to get $y = \frac{1}{5}x + 6$

Question

Find the gradient of a line that is perpendicular to 8y + 4x = 5.

▶️ Answer/Explanation

Answer: 2

First, find the gradient of the given line: rearrange to $y = -\frac{1}{2}x + \frac{5}{8}$ (gradient = $-\frac{1}{2}$). The perpendicular gradient is the negative reciprocal, so $2$.

CIE iGCSE Maths E3.7 Perpendicular lines Exam Style Practice Questions- Paper 2

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