Question

Point R is the midpoint of segment ST. If R is at (-7,3) and S is at (2,5). What are the coordinates of T? step -by-step please.

Answer 1

Since R is the midpoint of ST, we can use the midpoint formula to find the coordinates of T. The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the coordinates of the endpoints.

To find the x-coordinate of T, we add the x-coordinate of R to the difference between the x-coordinates of R and S.

x-coordinate of T = x-coordinate of R + (x-coordinate of R - x-coordinate of S)
x-coordinate of T = -7 + (-7 - 2)
x-coordinate of T = -7 - 9
x-coordinate of T = -16

To find the y-coordinate of T, we add the y-coordinate of R to the difference between the y-coordinates of R and S.

y-coordinate of T = y-coordinate of R + (y-coordinate of R - y-coordinate of S)
y-coordinate of T = 3 + (3 - 5)
y-coordinate of T = 3 - 2
y-coordinate of T = 1

Therefore, the coordinates of T are (-16, 1).

Answer 2

• T(- 16, 1)

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Given segment ST and midpoint R with coordinates:

• S( 2, 5),
• R(- 7, 3).

Find the coordinates of endpoint T with coordinates of (x , y) using midpoint formula:

• x-coordinate: - 7 = (x + 2)/2 ⇒ - 14 = x + 2 ⇒ x = - 16
• y-coordinate: 3 = (y + 5)/2 ⇒ 6 = y + 5 ⇒ y = 1

So, the point T has coordinates (- 16, 1).