Sue Pemberton Solutions for Chapter: Coordinate Geometry, Exercise 3: EXERCISE 3B

The midpoint of the line segment joining $P(-4,5)$ and $Q(6,1)$ is $M$. The point $R$ has coordinates $(-3,-7)$. Show that $RM$ is perpendicular to $PQ$.

Two vertices of a rectangle, $ABCD$, are $A(-6,-4)$ and $B(4,-8)$. Find the gradient of $CD$ and the gradient of $BC$.

The coordinates of three of the vertices of a trapezium, $ABCD$, are $A(3,5), B(-5,4)$ and $C(1,-5)$. $AD$ is parallel to $BC$ and angle $ADC$ is $90°$. Find the coordinates of $D$.

The coordinates of three points are $A(5,8), B(k, 5)$ and $C(-k, 4)$. Find the value of $k$ if $A, B$ and $C$ are collinear.

The vertices of triangle $ABC$ are $A(-9,2k-8), B(6, k)$ and $C(k, 12)$. Find the two possible values of $k$ if angle $ABC$ is $90°$.

$A$ is the point $(0,8)$ and $B$ is the point $(8,6)$. Find the point $C$ on the $y-$axis such that angle $ABC$ is $90°$.

The line $\frac{x}{a}-\frac{y}{b}=1$, where $a$ and $b$ are positive constants, meets the $x-$axis at $P$ and the $y-$axis at $Q$. The gradient of the line $PQ$ is $\frac{2}{5}$ and the length of the line $PQ$ is $2\sqrt{29}$. Find the value of $a$ and the value of $b$.