Question

if point a is (-2, -1) and point b is (3, 2), what is the distance between them? 7.21 6.08 8.54 5.83

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-2,y_1 = - 1,x_2=3,y_2 = 2$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=3-(-2)=5$ and $y_2 - y_1=2 - (-1)=3$.

Step3: Square the differences

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=3^2 = 9$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 9=34$.

Step5: Calculate the square - root

$d=\sqrt{34}\approx5.83$.

Answer:

5.83