Vectors - Intersection of Two Lines
Vectors - Intersection of Two Lines
Solutions to this question by accurate drawing will not be accepted.
The diagram above shows a quadrilateral \(ABCD\) with points \(A\left( 4,\text{}\hspace{0.5em}\frac{\text{7}}{\text{2}} \right)\), \(C\left( 2,-5 \right)\) and the point \(B\) on the \(x\)-axis. \(AD\) is perpendicular to \(DC\). Given that the gradient of \(AB\) is \(-\frac{1}{4}\) and the equation of \(AD\) is \(2y=x+3\), find
- the length of \(AB\), correct to \(3\) significant figures,
- the coordinates of \(D\),
- the area of \(ABCD\).
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Answer:(a) \(14.4\text{ units}\) (3 s.f.) (b) \(D=(-1,1)\) (c) \(81.75\text{ units}^2\)
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