# 8.2.1 Coordinates, PT3 Focus Practice

8.2.1 Coordinates, PT3 Focus Practice

Question 1
:
In diagram below, Q is the midpoint of the straight line PR.
The value of is

Solution
:
$\begin{array}{l}\frac{2+m}{2}=5\\ 2+m=10\\ \text{}m=8\end{array}$

Question 2:
In diagram below, P and Q are points on a Cartesian plane.

If M is the midpoint of PQ, then the coordinates of M are

Solution:

Question 3:
Find the distance between (–4, 6) and (20, –1).

Solution
:

Question 4:
Diagram shows a straight line PQ on a Cartesian plane.

Calculate the length, in unit, of PQ.

Solution
:
PS = 15 – 3 = 12 units
SQ = 8 – 3 = 5 units
By Pythagoras’ theorem,
PQ= PS2 + SQ2
= 122+ 52
PQ = √169
= 13 units

Question 5:
The diagram shows an isosceles triangle STU.

Given that ST = 5 units, the coordinates of point are

Solution
:

For an isosceles triangle STU, M is the midpoint of straight line TU.
Point M = (1, 0)

MT = 4 – 1 = 3 units
By Pythagoras’ theorem,
SM= ST2MT2
= 52 – 32
= 25 – 9
= 16
SM = √16
= 4
Therefore, point S = (1, 4).