Question

1. find cd given c(-6, -5) and d(2, 0). leave as a simplified radical.

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, $x_1=-6,y_1 = - 5,x_2=2,y_2 = 0$.

Step2: Substitute values

Substitute the values into the formula: $CD=\sqrt{(2-(-6))^2+(0 - (-5))^2}=\sqrt{(2 + 6)^2+(0 + 5)^2}=\sqrt{8^2+5^2}$.

Step3: Calculate squares and sum

First, calculate $8^2=64$ and $5^2 = 25$. Then $8^2+5^2=64 + 25=89$. So $CD=\sqrt{89}$.

Answer:

$\sqrt{89}$