AM Coordinate Geometry Practice Question 1
The figure shows a right-angled triangle $ABC$, where points $A$, $B$ and $C$ are $A\left( -2,8 \right)$, $\left( k,0 \right)$ and $\left( 10,4 \right)$ respectively. $AB$ cuts the $y$-axis at $P$. $Q$ is a point on $AC$ and $BC$ is parallel to $PQ$.
(i)
Given that $k<5$, find the value of $k$.
(ii)
Find the coordinates of $P$ and show that $P$ is the midpoint of $AB$.
(iii)
Hence find the coordinate of $Q$.
(iv)
$D$ is a point such that $ABCD$ is a rectangle. Find the coordinates of $D$.
(v)
Find the area of the rectangle $ABCD$.
(vi)
$F$ is a point on $BC$ such that $BF:FC=3:1$. Find the coordinates of $F$.
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