Question

find the distance between the pair of points. (-2, -5) and (-8,3)

a. 20
b. 10
c. 11
d. 100

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, $x_1=-2,y_1 = - 5,x_2=-8,y_2 = 3$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-8-(-2)=-8 + 2=-6$, and $y_2 - y_1=3-(-5)=3 + 5 = 8$.

Step3: Square the differences

Square the results from Step 2. $(x_2 - x_1)^2=(-6)^2 = 36$ and $(y_2 - y_1)^2=8^2=64$.

Step4: Sum the squares

Add the two squared - values: $(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 64=100$.

Step5: Take the square - root

$d=\sqrt{100}=10$.

Answer:

B. 10