Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint

formula, and solve the two equations for x and y.)
midpoint (-2, -16), endpoint (-7.-9)

Answer 1

Given:

One endpoint of a line segment = (-7,-9)

Midpoint of the segment = (-2,-16)

To find:

The other endpoint of the given line segment.

Solution:

Let (a,b) be the other endpoint of the given line segment.

Midpoint formula:

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

Using this formula, we get

`(-2,-16)=\left((-7+a)/(2),(-9+b)/(2)\right)`

On comparing both sides, we get

`(-7+a)/(2)=-2`

`-7+a=-4`

`a=-4+7`

`a=3`

And,

`(-9+b)/(2)=-16`

`-9+b=-32`

`b=-32+9`

`b=-23`

Therefore, the coordinates of other endpoint are (3,-23).