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
#((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