Answer:
y_2 is 8 units
Step-by-step explanation:
Given that
The distance between the point is 13 units
x_1 is 5
y_1 is 3
x_2 is -7
We need to find out the y_2
So, the following formula should be used
[tex]d = \sqrt({x_2 - x_1})^2 + (y_2 - y_1)^2\\\\13 = \sqrt({-7-5})^2 + (y_2 - 3)^2\\\\169 = 144 + (y_2)^2 + (-3)^2 - 2(y_2) (-3)\\\\25 = (y_2)^2 + 9 - 6y_2\\\\16 = (y_2)^2 -6y_2\\\\(y_2)^2 -6y_2 - 16 = 0\\\\(y_2)^2 - 8y_2 + 2y_2 - 16 = 0\\\\y_2 (y_2 - 8) + 2(y_2 - 8) = 0\\\\y_2 = 8[/tex]
hence, y_2 is 8 units
