the coordinates of point T are given. The midpoint of ST is (5,-8). Find the coordinates of point S.

18) T(10,18)

Given the coordinates of point T at (-5,6) and point X at (3,2). What is the coordinate for the midpoint of line segment TX?

To find the coordinates of point S, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) can be found by taking the average of the x-coordinates and the average of the y-coordinates.

Let's denote the coordinates of point S as (x, y). We know that the midpoint of ST is (5, -8), so we have:

Midpoint Formula:
(x₁ + x₂)/2 = 5
(y₁ + y₂)/2 = -8

Substituting the coordinates of point T (10, 18) and the unknown coordinates of point S (x, y), we get:

(x + 10)/2 = 5
(y + 18)/2 = -8

Now, let's solve these equations to find the values of x and y.

From the first equation, we can solve for x:

(x + 10)/2 = 5
x + 10 = 2 * 5
x + 10 = 10
x = 10 - 10
x = 0

From the second equation, we can solve for y:

(y + 18)/2 = -8
y + 18 = 2 * -8
y + 18 = -16
y = -16 - 18
y = -34

Therefore, the coordinates of point S are (0, -34).

Uuj

just note that S is the same distance from M (the midpoint) as T is.

So, for the x-coordinate, Mx-Sx = Tx-Mx
5-Sx = 10-5
5-Sx = 5
Sx = 0

Makes sense. We went from 10 to 5 to get from T to M. So, we have to drop another 5 to get to S: result is 0.

Now do the same for the y-coordinate