Question

ections: find the distance between (-4, 6) and (3, -7)
d = \sqrt{(6 - - 7)+(-4,3)}

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(-4,6)$ and $(x_2,y_2)=(3,-7)$.

Step2: Substitute values into formula

$d=\sqrt{(3-(-4))^2+((-7) - 6)^2}=\sqrt{(3 + 4)^2+(-13)^2}=\sqrt{49 + 169}$.

Step3: Calculate the sum inside square - root

$d=\sqrt{218}$.

Answer:

$\sqrt{218}$