# Given the midpoint(8,14) and one endpoint (-9,-1) of a line segment, find the other endpoint

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let the midpoint be m(8,14) and one endpoint be A(-9,-1)

Let the other end of the line segment  be B(x, y)

then  we know that:

xm = (xA+ xB)/2

ym = (yA+yB)/2

Let us subsitute:

==>  8 = (-9+x)/2

==> 16 = -9 + x

==> x = 16+ 9 = 25

==> x= 25

Now for y coordinate:

ym = (yA+yB)/2

14 = (-1+y)/2

28 = -1 + y

==> y= 28+ 1 = 29

==> y= 29

Then the other end point is B(25, 29)

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted on

To solve this question, you need two equations: the equation for a line, and the equation for the distance between two points. First, the line with the two points mentioned above is :

y = 15x/17 + 118/17

The distance between the two points is the sqrt(514).

Since the first point is the midpoint, you want to find a point on the line y with the same distance D = sqrt(514). The formula for distance from the first point is:

D^2 = (x - 8)^2 + (y - 14)^2

514 = x^2 - 16x + y^2 - 28y + 260, where y = 15x/17 + 118/17

Solve these two equations to get

x = 25, y = 29