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:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Using this formula, we get

$(-2,-16)=\left(\dfrac{-7+a}{2},\dfrac{-9+b}{2}\right)$

On comparing both sides, we get

$\dfrac{-7+a}{2}=-2$

$-7+a=-4$

$a=-4+7$

$a=3$

And,

$\dfrac{-9+b}{2}=-16$

$-9+b=-32$

$b=-32+9$

$b=-23$

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