Chapter 1, Problem 36RE

34. Find two numbers $y$ such that the distance from $\left(-3,2\right)$ to $\left(5,y\right)$ is 10.

To determine

To find: Two numbers $y$ such that the distance from $\left(-3, 2\right)\text{to}\left(5, y\right)$ is 10.

Answer to Problem 36RE

Solution:

$y = 8, -4$

Explanation of Solution

The distance between two points is $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}=10$

$\sqrt{{\left(5-\left(-3\right)\right)}^2+{\left(y-2\right)}^2} = 10$

$\sqrt{64+{\left(y-2\right)}^2}=10$

$64+{\left(y-2\right)}^2=100$

${\left(y-2\right)}^2=36$

$y-2=\pm 6$

$y=2+6, 2-6$

$y=8, -4$