Question

what is the distance, in units, between the points (-3,1) and (2,-1)?
○ √21
○ √3
○ √29
○ √5

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute given points

Let $(x_1,y_1)=(-3,1)$ and $(x_2,y_2)=(2,-1)$. Substitute into the formula:
$d=\sqrt{(2-(-3))^2+(-1-1)^2}$

Step3: Simplify the expressions inside

Calculate the differences:
$d=\sqrt{(5)^2+(-2)^2}$

Step4: Compute squares and sum

Calculate squares and add:
$d=\sqrt{25+4}=\sqrt{29}$

Answer:

$\sqrt{29}$ (Option: $\boldsymbol{\sqrt{29}}$)