Answer:
(-20, 19)
Step-by-step explanation:
We need to use the Midpoint Formula, which says that given two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the midpoint is [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex].
Here, we are given one of the endpoints and the midpoint:
endpoint S = (5, -8)
midpoint M = (-7.5, 5.5)
Plug these into the formula. In [tex]\frac{x_1+x_2}{2}[/tex], x1 = 5, and this whole expression is equal to -7.5:
[tex]\frac{x_1+x_2}{2}=\frac{5+x_2}{2} =-7.5[/tex]
Solve for x2:
5 + x2 = 2 * (-7.5) = -15
x2 = -15 - 5 = -20
Now, let's find y2. y1 is just -8, and the entire expression for the y-coordinate of the midpoint is equal to 5.5. So:
[tex]\frac{y_1+y_2}{2}=\frac{-8+y_2}{2} =5.5[/tex]
Solve for y2:
-8 + y2 = 2 * 5.5
-8 + y2 = 11
y2 = 11 + 8 = 19
The coordinates of T are thus (-20, 19).
~ an aesthetics lover
