Question

√((x₂ - x₁)+(y₂ - y₁)²) (1,0) (-4,-6)

Explanation:

Step1: Identify the distance - formula values

Let $(x_1,y_1)=(1,6)$ and $(x_2,y_2)=(-4,-6)$.

Step2: Substitute values into distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substituting the values, we get $d=\sqrt{(-4 - 1)^2+(-6 - 6)^2}$.

Step3: Calculate the values inside the square - root

First, $(-4 - 1)^2=(-5)^2 = 25$ and $(-6 - 6)^2=(-12)^2 = 144$. Then $(-4 - 1)^2+(-6 - 6)^2=25 + 144=169$.

Step4: Find the square - root

$d=\sqrt{169}=13$.

Answer:

$13$