7.2.2 Coordinates, PT3 Focus Practice

Question 4:
The point M (x, 4), is the midpoint of the line joining straight line Q (-2, -3) and R (14, y). The value of x and y are

Solution:

$\begin{array}{l}x=\frac{-2+14}{2}\\ x=\frac{12}{2}\\ x=6\\ \\ 4=\frac{-3+y}{2}\\ 8=-3+y\\ y=11\end{array}$

Question 5:

In diagram below, PQR is a right-angled triangle. The sides QR and PQ are parallel to the y-axis and the x-axis respectively. The length of QR = 6 units.
Given that M is the midpoint of PR, then the coordinates of M are

Solution:

x-coordinate of R = 3
y-coordinate of R = 1 + 6 = 7
R = (3, 7)

$\begin{array}{l}P\left(1,1\right),R\left(3,7\right)\\ \text{Coordinates of }M\\ =\left(\frac{1+3}{2},\frac{1+7}{2}\right)\\ =\left(2,4\right)\end{array}$

Question 6:

Given points P (–2, 8) and Q (10, 8), find the length of PQ.

Solution:

$\begin{array}{l}\text{Length of }PQ\\ =\sqrt{{\left[10-\left(-2\right)\right]}^2+{\left(8-8\right)}^2}\\ =\sqrt{{\left(12\right)}^2+0}\\ =12\text{ units}\end{array}$