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Exam-Style Question on Coordinate Geometry

A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 14. This question is similar to one that appeared on an IB Studies paper in 2010. The use of a calculator is allowed.

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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