Question

1. find the distance between the points (-3,-2) and (2, 5).

9.22
6.40
7.81
8.60

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, $x_1=-3,y_1 = - 2,x_2=2,y_2 = 5$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=2-(-3)=5$, $y_2 - y_1=5 - (-2)=7$.

Step3: Square the differences

$(x_2 - x_1)^2=5^2 = 25$, $(y_2 - y_1)^2=7^2=49$.

Step4: Sum and take square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{25 + 49}=\sqrt{74}\approx8.60$.

Answer:

8.60