Vectors - Intersection of Two Lines
Vectors - Intersection of Two Lines
Solutions to this question by accurate drawing will not be accepted.
The diagram shows a trapezium \(ABCD\) with parallel sides \(AB\) and \(DC\). Given that angle \(ABC\) and angle \(DCB\) are \(90{}^\circ \). The coordinates of \(A\), \(B\) and \(D\) are \(\left( 2,1 \right)\) , \(\left( 8,3 \right)\) and \(\left( 4,5 \right)\) respectively. Find
- the equation of \(DC\),
- the coordinates of \(C\),
- the coordinates of a point \(P\) on \(BD\) such that \(2BP=PD\),
- the area of the trapezium \(ABCD\).
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Answer:(a) \(y=\frac13x+\frac{11}{3}\) (b) \(C=(7,6)\) (c) \(P=\left(\frac{20}{3},\frac{11}{3}\right)\) (d) \(15\text{ units}^2\)
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