Question

1. Given that point M is the midpoint of AC , find the coordinates of the missing

endpoint when you are given one endpoint and the coordinates of the midpoint.

M(-2, 2) and A(2,8)

Answer 1

Given:

Coordinates of point A are (2,8).

Point M(-2,2) is the midpoint of AC.

To find:

The coordinates of C.

Solution:

Let the coordinates of point C are (a,b).

Formula for midpoint:

`Midpoint=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)`

Using the above formula, the midpoint of A(2,8) and C(a,b) is

`M=\left((2+a)/(2),(8+b)/(2)\right)`

`(-2,2)=\left((2+a)/(2),(8+b)/(2)\right)`

On comparing both sides, we get

`(2+a)/(2)=-2`

`2+a=-4`

`a=-4-2`

`a=-6`

and,

`(8+b)/(2)=2`

`8+b=4`

`b=4-8`

`b=-4`

Therefore, the coordinates of point c are (-6,-4).