Question

what is the distance between points (1,2) and (4,-5)?

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinates

Here $x_1 = 1,y_1 = 2,x_2 = 4,y_2=-5$.

Step3: Substitute values

$d=\sqrt{(4 - 1)^2+(-5 - 2)^2}=\sqrt{3^2+(-7)^2}=\sqrt{9 + 49}=\sqrt{58}$.

Answer:

$\sqrt{58}$