Question

What is the approximate distance between the points (-3,-4) and (-8,1) on a coordinate grid?

Answer 1

Answer:

$5\sqrt{2}$

Step-by-step explanation:

The distance between two points on a Cartesian coordinate grid is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$ where $d$ is the distance between $(x_1,y_1)\rightarrow(-3,-4)$ and $(x_2,y_2)\rightarrow(-8,1)$:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-8-(-3))^2+(1-(-4))^2}\\\\d=\sqrt{(-8+3)^2+(1+4)^2}\\\\d=\sqrt{(-5)^2+5^2}\\\\d=\sqrt{25+25}\\\\d=\sqrt{50}\\\\d=5\sqrt{2}$

Therefore, the distance between the two points is $5\sqrt{2}$ units.