Question

How do you find the missing endpoint if P is the midpoint of line NQ

N(2,0) P(5,2)

Answer 1

`coordinates\ of\ Q(x,y)\\\\ P(5,2)=((2+x)/(2)\ ;\ (0+y)/(2))\\\\5=(2+x)/(2)\ \ |*2\\\\10=2+x\\\\ 10-2=x\\\\x=8\\\\ 2=(0+y)/(2)\ \ |*2\\\\ 4=y\\\\ Q=(8,4)`

Answer 2

`N(2,0),\ \ Q(x,y) \ \ midpoint : P(5,2)\\\\ Given \ the \ two \ points \ (x _(1), y _(1)) and (x _(2), y _(2)), \\the \ midpoint \ is \ given \ by \ the \ formula: \\\\ (x,y)=((x_(1)+x_(2))/(2);(y_(1)+y_(2))/(2))\\\\(5,2)=((2+ x)/(2);(0+y)/(2)) (2+ x)/(2)=5 \ \`


`(2+ x)/(2)=5 \ \ |\ multiply\ both\ sides\ by\ 2 \\\\2+x=10\ \ |\ subtract\ 2 \ to\ both\ sides \\\\x=8`


`(0+y)/(2)=2 \ \ |\ multiply\ both\ sides\ by\ 2 \\\\y=4 \\\\Answer: \ Q (8,4)`