Answer:
coordinates of point S are (12, -24)
Explanation:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, the midpoint is (5, -8), and point T is (-2, 8). So, you have:
Midpoint = ((x + (-2)) / 2, (y + 8) / 2)
Now, you can plug in the values for the midpoint:
5 = (x - 2) / 2
-8 = (y + 8) / 2
First, solve for x:
5 = (x - 2) / 2
Multiply both sides by 2 to isolate x:
10 = x - 2
Now, add 2 to both sides to find x:
x = 10 + 2
x = 12
Now that you have x, you can solve for y using the second equation:
-8 = (y + 8) / 2
Multiply both sides by 2 to isolate y:
-16 = y + 8
Subtract 8 from both sides to find y:
y = -16 - 8
y = -24
So, the coordinates of point S are (12, -24).