Question

#8 find the distance between (-2, -6) and (3, -4) using the formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Explanation:

Step1: Identify the coordinates

Let $(x_1,y_1)=(-2,-6)$ and $(x_2,y_2)=(3,-4)$.

Step2: Substitute into distance formula

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(3-(-2))^2+((-4)-(-6))^2}$

Step3: Simplify the expressions inside the square - root

First, $3-(-2)=3 + 2=5$ and $(-4)-(-6)=-4 + 6 = 2$. Then $d=\sqrt{5^2+2^2}=\sqrt{25 + 4}=\sqrt{29}$.

Answer:

$\sqrt{29}$