Question

1. find the distance between the two points. x (-3, -2) and y (-6, 5)

√58
2√17
3√10
√122

Explanation:

Step1: Identify distance formula

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

Step2: Substitute the given points

Here, $x_1=-3,y_1 = - 2,x_2=-6,y_2 = 5$. So $d=\sqrt{(-6-(-3))^2+(5 - (-2))^2}$.

Step3: Simplify the expressions inside the square - root

First, $-6-(-3)=-6 + 3=-3$ and $5-(-2)=5 + 2 = 7$. Then $d=\sqrt{(-3)^2+7^2}=\sqrt{9 + 49}=\sqrt{58}$.

Answer:

$\sqrt{58}$