Answer:
a. The y coordinates for A are either 10 or -14
b. The y coordinates for A are either -11 or 7
Explanation:
distance = sqrt ((x2-x1)^2+(y2-y1)^2)
We know Point B and the x coordinate of point A as well as the distance
15 = sqrt ((-4-5)^2+(-2-y1)^2)
15 = sqrt ((-9)^2+(-2-y1)^2)
15 = sqrt (81+(-2-y1)^2)
Square each side
15^2 =sqrt (81+(-2-y1)^2)^2
225 = 81+(-2-y1)^2
Subtract 81 from each side
225-81 = 81-81 +(-2-y1)^2
144 = (-2-y1)^2
Take the square root of each side
±sqrt 144 = sqrt(-2-y1)^2
±12 = (-2-y1)
Add 2 to each side
2±12 = 2-2-y1
2±12 = -y1
14 = -y1 or -10 = -y1
Multiply by -1
-14 = y1 or 10 = y1
The y coordinates for A are either 10 or -14
Now move B to -7,-2
15 = sqrt ((-7-5)^2+(-2-y1)^2)
15 = sqrt ((-12)^2+(-2-y1)^2)
15 = sqrt (144+(-2-y1)^2)
Square each side
15^2 =sqrt (144+(-2-y1)^2)^2
225 = 144+(-2-y1)^2
Subtract 144 from each side
225-144 = 144-144 +(-2-y1)^2
81 = (-2-y1)^2
Take the square root of each side
±sqrt 81 = sqrt(-2-y1)^2
±9 = (-2-y1)
Add 2 to each side
2±9 = 2-2-y1
2±9 = -y1
11 = -y1 or -7 = -y1
Multiply by -1
-11 = y1 or 7 = y1
The y coordinates for A are either -11 or 7