Given:
Midpoint = (2,-14)
One endpoint = (4,-13)
To find:
The another endpoint.
Solution:
Let (a,b) be the another endpoint.
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
Using midpoint formula, we get
[tex](2,-14)=\left(\dfrac{a+4}{2},\dfrac{b+(-13)}{2}\right)[/tex]
[tex](2,-14)=\left(\dfrac{a+4}{2},\dfrac{b-13}{2}\right)[/tex]
On comparing both sides, we get
[tex]2=\dfrac{a+4}{2}[/tex]
[tex]4=a+4[/tex]
[tex]4-4=a[/tex]
[tex]0=a[/tex]
And,
[tex]-14=\dfrac{b-13}{2}[/tex]
[tex]-28=b-13[/tex]
[tex]-28+13=b[/tex]
[tex]-15=b[/tex]
Therefore, the another endpoint is (0,-15).
