# Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams.

### 1.

GCSE Higher

Show that line $$5y = 7x - 7$$ is perpendicular to line $$7y = -5x + 55$$.

### 2.

IB Studies

The vertices of quadrilateral ABCD are A (2, 4), B (-1, 5), C (–3, 4) and D (–2, 2).

(a) Calculate the gradient of line CD.

(b) Show that line AD is perpendicular to line CD.

(c) Find the equation of line CD. Give your answer in the form $$ax+by=c$$ where $$a,b,c\in \mathbf Z$$

Lines AB and CD intersect at point E.

(d) Find the coordinates of E.

(e) Find the distance between A and D.

The distance between D and E is $$\sqrt{20}$$.

(f) Find the area of triangle ADE.

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