The midpoint M of TU has coordinates (6, 4). Point U has coordinates (10, 3). Find the coordinates of point T.

Answer 1

T (2, 5)

Use the midpoint formula with coordinates of points U and T (x_U, y_U) and (x_M, y_M) respectively to solve for the coordinates of T

Lets call them (x_T, y_T)

Midpoint formula {(x_U + x_T)/2, (y_U + y_T)/2)}

Plug in the known coordinates where appropriate

Point U at (10, 3) = (x_U, y_U)

Midpoint, point M at (6, 4) = (x_M, y_M)

For the x coordinates

(10 + x_T)/2 = 6

Multiply both sides of the equation by 2

10 + x_T = 12

Subtract 10 from both sides of the equation

x_T = 2

Do the same for the y coordinate

(3 + y_T)/2 = 4

3 + y_T = 8

y_T = 5

We can check by using the coordinates of T in the midpoint formula

(10 + 2)/2 = 12/2 = 6

(5 + 3)/2 = 8/2 = 4

I hope you find this useful please send a message if you have any questions.