Question

The midpoint M and one endpoint of GH are given.find the coordinates of the other endpoint

Answer 1

Answer:

(3,12)

Step-by-step explanation:

Let the coordinates of H be (x,y).

$\frac{5+x}{2}=4 \implies x=3 \\ \\ \frac{-6+y}{2}=3 \implies y=12 \\ \\ \therefore H=(3,12)$

Answer 2

The midpoint of a line segment means a point that lies in the mid of the given line segment. The coordinates of the other endpoint H are (3,12).

What does a midpoint mean?

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point that lies in the mid of the given line segment.

The x-coordinate of the point H is,

$x_m = \dfrac{x_G+x_H}{2}\\4 = \dfrac{5 + x_H }{2}\\\\8 = 5 + x_H\\\\x_H = 3$

The y-coordinate of the point H is,

$y_m = \dfrac{y_G+y_H}{2}\\3 = \dfrac{-6 +y_H }{2}\\\\6 = -6 + y_H\\\\y_H =12$

Hence, the coordinates of the other endpoint H are (3,12).

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