Question

find the distance between the pair of points. 13) (-5, -1) and (-11, -9)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Let $(x_1,y_1)=(-5,-1)$ and $(x_2,y_2)=(-11,-9)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=-11-(-5)=-11 + 5=-6$.
$y_2 - y_1=-9-(-1)=-9 + 1=-8$.

Step3: Square the differences

$(x_2 - x_1)^2=(-6)^2 = 36$ and $(y_2 - y_1)^2=(-8)^2 = 64$.

Step4: Sum and square - root

Sum the squared differences: $(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 64 = 100$.
Then $d=\sqrt{100}=10$.

Answer:

$10$