Coordinate Geometry
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 $F$.
(i)
(ii)
(iii)
(iv) 
(v) 
(vi) 
Question 2
Given that the $x$- intercept of a line is twice its $y$- intercept and that the line passes through the point of intersection of the lines $3y+x=3$ and $4y-3x=5$, find the equation of this line.
Question 3
The diagram shows a quadrilateral $ABCD$ where $A$ is $\left( 6,1 \right)$, $B$ lies on the $x$-axis and $C$ is $\left( 1,3 \right)$. The diagonal $BD$ bisects $AC$ at right angles at $M$. Find
(i)
the equation of $BD$,
(ii)
the coordinates of $B$,
(iii)
the coordinates of $D$ such that $ABCD$ is a parallelogram.
(i) 
(ii) 
(iii) 