Question

find the distance between a (-1,2) and b (-4,6).

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, $x_1=-1,y_1 = 2,x_2=-4,y_2 = 6$.

Step2: Substitute values

$d=\sqrt{(-4-(-1))^2+(6 - 2)^2}=\sqrt{(-4 + 1)^2+4^2}=\sqrt{(-3)^2+4^2}$.

Step3: Calculate squares and sum

$\sqrt{(-3)^2+4^2}=\sqrt{9 + 16}=\sqrt{25}$.

Step4: Find square - root

$\sqrt{25}=5$.

Answer:

$5$