Question

find the distance between each pair of points. remember to simplify the radical.

1. (5, -8), (-1, 6)
2. (4, -4), (4, 1)

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: Solve for the first - pair of points $(5,-8)$ and $(-1,6)$

Let $(x_1,y_1)=(5,-8)$ and $(x_2,y_2)=(-1,6)$.
First, calculate $(x_2 - x_1)$ and $(y_2 - y_1)$:
$x_2 - x_1=-1 - 5=-6$;
$y_2 - y_1=6-( - 8)=6 + 8 = 14$.
Then, $d=\sqrt{(-6)^2+14^2}=\sqrt{36 + 196}=\sqrt{232}=\sqrt{4\times58}=2\sqrt{58}$.

Step3: Solve for the second - pair of points $(4,-4)$ and $(4,1)$

Let $(x_1,y_1)=(4,-4)$ and $(x_2,y_2)=(4,1)$.
$x_2 - x_1=4 - 4 = 0$;
$y_2 - y_1=1-( - 4)=1 + 4 = 5$.
Then, $d=\sqrt{(0)^2+5^2}=\sqrt{0 + 25}=5$.

Answer:

1. $2\sqrt{58}$
2. $5$