Solutions to this question by accurate drawing will not be accepted. In the diagram, $ABCD$ is a t

Question

Solutions to this question by accurate drawing will not be accepted. In the diagram, $ABCD$ is a trapezium where $AD$ and $BC$ are parallel to the $y$-axis and $AB$ is parallel to the $x$-axis. $D$ is the point $(-4, 7)$ and $C$ is the point $(5, 9)$. The line $DC$ cuts the $y$-axis at $Q$. Find the equation of the line $CD$, Find the coordinates of $Q$, Given the area of the trapezium is $162$ units$^2$, find the coordinates of point $B$, Hence, find the equation of the line $AC$.

Accepted Answer

(a) $y=\frac29x+\frac{71}{9}$; (b) $\left(0,\frac{71}{9}\right)$; (c) $(5,-10)$; (d) $y=\frac{19}{9}x-\frac{14}{9}$.

Coordinate Geometry - Area of Rectilinear Figures

Coordinate Geometry - Area of Rectilinear Figures

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