1.11: The points and have coordinates and respectively.

The points $\displaystyle A$ and $\displaystyle B$ have coordinates $\displaystyle (1, 5)$ and $\displaystyle (9, 9)$ respectively.

(a) Find an equation of line $\displaystyle AB$, giving your answer in the form $\displaystyle ax + by + c = 0$, where $\displaystyle a, b$ and $\displaystyle c$ are integers to be found.

The line $\displaystyle l$ is perpendicular to $\displaystyle AB$ and passes through the point $\displaystyle X$ which lies on $\displaystyle AB$ such that $\displaystyle AX : XB = 3:1$

(b) Show that an equation of $\displaystyle l$ is $\displaystyle y = -2x + 22$

The point $\displaystyle C$ has coordinates $\displaystyle (6, p)$

Given that $\displaystyle C$ lies on $\displaystyle l$

(c) find the value of $\displaystyle p$

$\displaystyle ABCD$ is a parallelogram where the $\displaystyle x$ coordinate of $\displaystyle D$ is negative.

(d) Find the coordinates of the point $\displaystyle D$

(e) Find the area of the parallelogram $\displaystyle ABCD$