How to find other endpoint given one and a midpoint

Asked by admin @ 04/12/2021 in Mathematics viewed by 447 People

What is the formula to find an endpoint when you are given one endpoint and the midpoint?

example: Find the missing endpoint if S is the midpoint RT.R(-9, 4) and S(2, -1); Find T

Answered by admin @ 04/12/2021

Answer:

Step-by-step explanation:

If S is the midpoint of R and S and the coordinate R(-9, 4) and S(2, -1), we are to find T.

Usimg the midpoint formula;

$M(X, Y) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\\ where; X = \frac{x_1+x_2}{2}\\Y = \frac{y_1+y_2}{2}$

Given $x_1 = -9, y_1 = 4, X = s \ and \ Y = -1$ , to get the other coordinate T (x2, y2), we will use the formula above as shown;

$X = \frac{x_1+x_2}{2}\\2 = \frac{-9+x_2}{2}\\cross \ multiply\\2*2 = -9+x_2\\4 = -9+x_2\\x_2 = 4+9\\ x_2 = 13$

Similarly to get y2;

Y = y1+y2/6

-1 = 4+y2/2

cross multiply

-1*2 = 4+y2

-2 = 4+y2

y2 = -2-4

y2 = -6

Hence the coordinate T is (13, -6)

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