Question

find the distance between the points c(-6, 5) and d(-3, 1). the distance between the two points is

Explanation:

Step1: Identify the distance - formula

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

Step2: Assign the values of the points

Let $(x_1,y_1)=(-6,5)$ and $(x_2,y_2)=(-3,1)$. Then $x_2 - x_1=-3-(-6)=-3 + 6 = 3$ and $y_2 - y_1=1 - 5=-4$.

Step3: Calculate the squares

$(x_2 - x_1)^2=3^2 = 9$ and $(y_2 - y_1)^2=(-4)^2 = 16$.

Step4: Sum the squares and take the square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Answer:

5