1 Determine the co-ordinate of M the midpoint of line RT. 3.2 Calculate the gradient of the line WT. 3.3 Prove that RW is perpendicular to WT.

To find the midpoint M of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$, we use the formula:

Given R($-5, 3$) and T($6, 6$).

To calculate the gradient $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$, we use the formula:

Given W($-3, 0$) and T($6, 6$).

For two lines to be perpendicular, the product of their gradients must be $-1$. We already have $m_{WT} = \frac{2}{3}$. Now we need to calculate the gradient of RW.
Given R($-5, 3$) and W($-3, 0$).

In a parallelogram, the diagonals bisect each other, meaning they share a common midpoint. The diagonals of RWTK are RT and WK. We already found the midpoint of RT in 3.1 as $M_{RT} = \left(\frac{1}{2}, \frac{9}{2}\right)$.
Now we find the midpoint of WK using W($-3, 0$) and K($a, b$).