Question

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

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

Step3: Calculate the values inside the square - root

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

Step4: Simplify the square - root

$d=\sqrt{58}$.

Answer:

$\sqrt{58}$