Solutions to this question by accurate drawing will not be accepted. The diagram shows a right-angle

Question

Solutions to this question by accurate drawing will not be accepted. The diagram shows a right-angled triangle $ABC$ where $\angle ABC = 90^\circ$. The coordinates of $A$ and $B$ are $(-8, -4)$ and $(4, 14)$ respectively. Find the equation of the line $BC$. Find the coordinates of $P$ and of $Q$, where $P$ lies on the $y$-axis and $Q$ is the intersection of line $BC$ and the $x$-axis. Given that $BC = 2AB$, find the coordinates of $C$. Find the area of the quadrilateral $APQC$.

Accepted Answer

(i) $y=-\dfrac23x+\dfrac{50}{3}$ (ii) $P=(0,8),\ Q=(25,0)$ (iii) $C=(40,-10)$ (iv) $377\text{ units}^2$.

Coordinate Geometry - Length of a Line Segment

Coordinate Geometry - Length of a Line Segment

Solution:

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