P is the point (-3, 1) and Q is the point (3, 3).

(a)
Find the length of the PQ.
(b)
The point R is such that PQR forms an isosceles triangle.
The angle bisector of angle PQR has an equation of $y = x$ .
Find the coordinates of R.

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Worked solution

1. Find the horizontal and vertical differences between P and Q.

For $P(-3,1)$ and $Q(3,3)$ ,

horizontal difference $=3-(-3)=6$

vertical difference $=3-1=2$

2. Apply the distance formula to find $PQ$.

$PQ=\sqrt{6^2+2^2}$
$=\sqrt{36+4}$
$=\sqrt{40}$
$=2\sqrt{10}$

Answer

$PQ=2\sqrt{10}$ units

AI analysis — may contain mistakes.

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