Advanced coordinate geometry: Determining Area from Coordinates
Advanced coordinate geometry: Determining Area from Coordinates
Solutions to this question by accurate drawing will not be accepted.
The diagram shows a quadrilateral \(ABCD\) in which \(A\) is \(\left( 2,5 \right)\), \(B\) is \(\left( 4,-1 \right)\) and point \(C\) is on the \(y\)-axis.
- Find the gradient of the line perpendicular to \(AB\).
- If the perpendicular bisector of \(AB\) cuts the \(y\)-axis at \(C\), find the coordinates of \(C\).
- Find the coordinates of \(D\) if \(ABCD\) is a parallelogram.
- Calculate the area of the parallelogram \(ABCD\).
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Answer:(a) \(\frac13\) (b) \(C=(0,1)\) (c) \(D=(-2,7)\) (d) \(20\text{ units}^2\)
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