Question

A line segment has a midpoint of (7, 1/2) If one endpoint is (5,3), what is the other endpoint?

Answer 1

Answer:

$\textbf{The co-ordinates of the other end point: (x_2,y_2) = (9,-2) }$

Step-by-step explanation:

$The Mid point(M) of (x_1,y_1) and (x_2,y_2) is given as M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right ) \\Call (5,3) as (x_1,y_1) and the other end point that is to be determined as (x_2,y_2) \\Now, from the mid point formula we have, 7 = \frac{5 + x_2}{2} \hspace{5mm}, \hspace{5mm} \frac{1}{2} = \frac{3 + y_2}{2} On Simplyfying, We have \textbf{ (x_2,y_2) = (9,-2) }$

Answer 2

So if 7 is the middle x-value, you calculate how far it is from the given endpoint in order to determine how far it is from the other endpoint. So,

7 -5 =2, so the other endpoint must be 2 away from 7 in the opposite direction, 7+2=9

Then repeat with y,

3-1/2=5/2, therefore 1/2 - 5/2 = -4/2= -2

So the point is (9, -2)