Answer: Point Q is closer
===========================================
Explanation:
Use the distance formula to calculate the length of segment PQ
[tex]P = (x_1,y_1) = (3,2) \text{ and }Q = (x_2,y_2) = (8,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-8)^2 + (2-6)^2}\\\\d = \sqrt{(-5)^2 + (-4)^2}\\\\d = \sqrt{25 + 16}\\\\d = \sqrt{41}\\\\d \approx 6.40312\\\\[/tex]
PQ is roughly 6.403 units long.
Repeat the same type of calculations, but this time we want to find the length of segment PR.
[tex]P = (x_1,y_1) = (3,2) \text{ and }R = (x_2,y_2) = (4,-5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-4)^2 + (2-(-5))^2}\\\\d = \sqrt{(3-4)^2 + (2+5)^2}\\\\d = \sqrt{(-1)^2 + (7)^2}\\\\d = \sqrt{1+49}\\\\d = \sqrt{50}\\\\d \approx 7.07107\\\\[/tex]
--------------------
To summarize, we have these approximate segment lengths.
Segment PQ is shorter, which means Q is the closer point.
