find all values find all values of y such that the distance between (6,y) and (-8,9) is 24

Question

find all values of y such that the distance between (6,y) and (-8,9) is 24

Answer 1

(-8,9), (6,y)

use the pythagorean theorem or the distance formula

d^2 = a^2 + b^2

24^2 = (-8-6)^2 + (9-y)^2

24^2= 14^2 + (y-9)^2

576-196 =(y-9)^2

(y-9)^2 = 380

take square roots of both sides

y-9 = +/-sqr380

y = 9+/-2sqr95

y= about 9+/- 19.5

y = about 9-19.5 or 9+19.5

y = about -10.5 or 28.5

it might help to plot the points

and draw a right triangle with vertices (-8,9), (6,-10.5), (6.9)

and another right triangle with vertices (-8,9), (6,28.5), (6,9)

calculate the hypotenuses of the triangles= about 24