A triangle has vertices P, Q and R - Edexcel - GCSE Maths - Question 19 - 2017 - Paper 2

The coordinates of Q are (1, 4) and R are (5, -2).

The midpoint N can be calculated using the same formula:

$N = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Thus,

$N = \left( \frac{1 + 5}{2}, \frac{4 - 2}{2} \right) = \left( 3, 1 \right)$

The coordinates of M are (-1, -1) and N are (3, 1).

The gradient of MN is given by:

$\text{Gradient of } MN = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-1)}{3 - (-1)} = \frac{2}{4} = \frac{1}{2}$

The coordinates of P are (-3, -6) and R are (5, -2).

The gradient of PR is:

$\text{Gradient of } PR = \frac{-2 - (-6)}{5 - (-3)} = \frac{4}{8} = \frac{1}{2}$

Since the gradients of MN and PR are equal, i.e., both are ( \frac{1}{2} ), we can conclude that:

$MN \parallel PR$

Thus, MN is parallel to PR.