Question

find the distance between the points c( - 6,5) and d( - 2,1). the distance between the two points is

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, $x_1=-6,y_1 = 5,x_2=-2,y_2 = 1$.

Step2: Calculate differences

First, find $x_2 - x_1=-2-(-6)=-2 + 6=4$ and $y_2 - y_1=1 - 5=-4$.

Step3: Square the differences

$(x_2 - x_1)^2=4^2 = 16$ and $(y_2 - y_1)^2=(-4)^2 = 16$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=16 + 16=32$.

Step5: Take square - root

$d=\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$.

Answer:

$4\sqrt{2}$