Question

directions: find the distance between each pair 1. (-4, 6) and (3, -7)

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: Assign values

Let $(x_1,y_1)=(-4,6)$ and $(x_2,y_2)=(3,-7)$. Then $x_2 - x_1=3-(-4)=7$ and $y_2 - y_1=-7 - 6=-13$.

Step3: Calculate squares

$(x_2 - x_1)^2=7^2 = 49$ and $(y_2 - y_1)^2=(-13)^2 = 169$.

Step4: Sum squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=49 + 169=218$.

Step5: Find square - root

$d=\sqrt{218}$.

Answer:

$\sqrt{218}$