Solutions to this question by accurate drawing will not be accepted. The diagram above shows a trape

Question

Solutions to this question by accurate drawing will not be accepted. The diagram above shows a trapezium $ABCD$ in which $AB$ is parallel to $CD$. The points $A$ and $C$ lie on the $x$-axis and the points $B$ and $D$ lie on the $y$-axis. The equation of $AB$ is $2y=x+8$ and the coordinates of $A$, $B$ and $C$ are $\left( -8,0 \right)$, $\left( 0,4 \right)$ and $\left( 2,0 \right)$ respectively. Show that the coordinate of $D$ is $\left( 0,-1 \right)$. Find the equation of the perpendicular bisector of $CD$. If $N$ is a point on $AB$ which is equidistant from $C$ and $D$, find the coordinates of $N$. Find the area of $ABCD$. Hence, find the perpendicular distance from $A$ to $CD$ produced. Correct your answer to $3$ significant figures.

Accepted Answer

(a) $D=(0,-1)$ (b) $y=-2x+\frac32$ (c) $N=\left(-1,\frac72\right)$ (d) $25\text{ units}^2$ (e) $4.47\text{ units}$ (3 s.f.)

Vectors - Intersection of Two Lines

Vectors - Intersection of Two Lines

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