Answer: (-16, 14)
Step-by-step explanation:
We know that the coordinates of mid point of a line segment having end points (a,b) and (m,n) is given by :-
[tex]x=\dfrac{a+m}{2}\ \ ,\ \ y=\dfrac{b+n}{2}[/tex]
Given : The midpoint of MN is point P at (-4, 6). If point M is at (8, -2).
Let the coordinates of N be (a,b).
Then by using the above formula, we have
[tex]-4=\dfrac{8+a}{2}\ \ ,\ \ 6=\dfrac{-2+b}{2}[/tex]
[tex]\Rightarrow\ -8=8+a\ \ ,\ \ 12=-2+b[/tex] [Multiplying 2 on both sides]
[tex]\Rightarrow\ a=-8-8=-16\ \ ,\ \ b=12+2=14[/tex]
Hence, the coordinates of point N = (-16, 14)
