Find the missing endpoint Given the other endpoint and midpoint .

Question

Endpoint: (-5,10)

Midpoint: (2,9)

Answer 1

I have derived two formulas for you.
They are:

x = Mx +or- D/sqrt(M^2 + 1)
y = m(x - Mx) + My

where Mx is the x-coordinate of the midpoint,
My is the y-coordinate of the midpoint,
M is the slope
D is the distance from the midpoint to the given endpoint

In this problem

Mx = 2

D = sqrt( 1 + 49) = sqrt(50) = 5*sqrt(2)

M = -1/7


x = Mx +or- D/sqrt(M^2 + 1)

= 2 +or- 5*sqrt(2) / sqrt( 50/49)

= 2 +or- 5*sqrt(2) / ( 5*sqrt(2)/7)

= 2 +or- 7

X = 2 + 7 = 9


x = 2 - 7 = -5 which is the x-coordinate of given point.

So x=9 which per the second formula means y = (-1/7)(9 - 2)+ 9
= (-1/7)(7) + 9
= -1 + 9 = 8

So the other endpoint is (9,8).
It works! THe slope of (9,8) and (2,9) is (-1/7)
and their distance is square root of 50
It also works on the other problem I did for you.