# What is the Endpoint Formula?

##### 1 Answer

Let's say you had one midpoint given. If you had *neither* endpoint given nor another midpoint given, then there are an infinite number of endpoints possible and your point is arbitrarily placed (because you only have one point available).

*So, to find an endpoint, you need one endpoint and a designated midpoint.*

Suppose you have midpoint

#x_1 = 1#

#y_1 = 2#

So what are **midpoint of a line segment** is based on *averaging* both coordinates in each dimension, assuming 2D cartesian:

#((x_1 + x_color(red)(2))/color(red)(2), (y_1 + y_color(red)(2))/color(red)(2))# where an average is defined as:

#[a_1 + a_2 + a_3 + ... + a_color(red)(N)]/color(red)(N)#

Therefore, you can plug in what you know here to find

#M(5,7) = ((x_1 + x_2)/2, (y_1 + y_2)/2)#

#5 = (x_1 + x_2)/2 => 10 = 1 + x_2#

#color(green)(x_2 = 9)#

#7 = (y_1 + y_2)/2 => 14 = 2 + y_2#

#color(green)(y_2 = 12)#

Therefore, your line segment passes through