The diagram shows a trapezium $ABCD$ in which $A$ is $(1,\ 2)$, $B$ is $(5,\ 10)$ and \(D\

Question

The diagram shows a trapezium $ABCD$ in which $A$ is $(1,\ 2)$, $B$ is $(5,\ 10)$ and $D$ is $(9,\ 3)$. Angle $ABC$ is $90^\circ$ and $AB$ is parallel to $DC$. Find the equation of $CD$.[2] Find the equation of $BC$.[2] Hence find the coordinates of $C$.[2] Find the area of the trapezium $ABCD$.[3] The point $E$ lies on $AC$ such that $AE : EC = 3 : 2$. Find the coordinates of $E$.[2]

Accepted Answer

(a) $y=2x-15$; (b) $x+2y=25$; (c) $(11,7)$; (d) $45$ units$^2$; (e) $(7,5)$.

Right-angled trapezium and a point dividing a diagonal

Right-angled trapezium and a point dividing a diagonal

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