Question

1. find the distance cd of c(-6, 4) and d(-3, -2)

Explanation:

Step1: Identify 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, $x_1=-6,y_1 = 4,x_2=-3,y_2=-2$.

Step2: Substitute values

Substitute the values into the formula: $d=\sqrt{(-3-(-6))^2+(-2 - 4)^2}=\sqrt{(-3 + 6)^2+(-6)^2}=\sqrt{3^2+(-6)^2}$.

Step3: Calculate squares and sum

First, calculate the squares: $3^2 = 9$ and $(-6)^2=36$. Then find the sum: $\sqrt{9 + 36}=\sqrt{45}$.

Step4: Simplify square - root

$\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}$.

Answer:

$3\sqrt{5}$