## Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. |

## 1. | GCSE Higher |

The equation of the line L_{1} is \(y = 2 - 5x\).

The equation of the line L_{2} is \(3y + 15x + 17 = 0\).

Show that these two lines are parallel.

## 2. | GCSE Higher |

Which of the following lines is parallel to the x-axis?

\(y=-7\)

\(x-y=1\)

\(x=10\)

\(x+y=0\)

\(x=y\)

## 3. | GCSE Higher |

Show that line \(5y = 7x - 7\) is perpendicular to line \(7y = -5x + 55\).

## 4. | GCSE Higher |

Suppose a rhombus ABCD is drawn on a coordinate plane with the point A situated at (4,7). The diagonal BD lies on the line \(y = 2x - 5 \)

Find the equation the line that passes through A and C.

## 5. | 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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