Question

Point P has coordinates (-4, -2) and point Q has coordinates (4, 3).

Calculate the shortest distance between P and Q.
Give your answer to 1 decimal place.
cm grid
-4 -3 -2
P
4
3
2
-2-
-3
4
2
D

Answer 1

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad Q(\stackrel{x_2}{4}~,~\stackrel{y_2}{3})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ PQ=√((~~4 - (-4)~~)^2 + (~~3 - (-2)~~)^2)\implies PQ=√((4 +4)^2 + (3 +2)^2) \\\\\\ PQ=√( (8)^2 + (5)^2) \implies PQ=√( 64 + 25)\implies PQ=√( 89 )\implies PQ\approx 9.4`