Question

1. find the length between a(-4, -5) and b(1, -2).

Explanation:

Step1: Identify distance - formula

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

Step2: Substitute the values

Here, $x_1=-4,y_1 = - 5,x_2=1,y_2=-2$. So $d=\sqrt{(1-(-4))^2+((-2)-(-5))^2}$.

Step3: Simplify the expressions inside the square - root

First, $1-(-4)=1 + 4=5$ and $(-2)-(-5)=-2 + 5 = 3$. Then $d=\sqrt{5^2+3^2}=\sqrt{25 + 9}=\sqrt{34}$.

Answer:

$\sqrt{34}$