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Exam-Style Question on Coordinate GeometryA mathematics exam-style question with a worked solution that can be revealed gradually |
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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