Question

A line segment has a midpoint of (7, 1/2)

If one endpoint is (5,3), what is the other endpoint?

Answer 1

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)

Answer 2

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

Explanation:

`The Mid point(M) of $(x_1,y_1)$and $(x_2,y_2)$is given as $$M = \left( (x_1 + x_2)/(2), (y_1 + y_2)/(2) \right )$$\\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, $$7 = (5 + x_2)/(2) \hspace{5mm}, \hspace{5mm} (1)/(2) = (3 + y_2)/(2)$$On Simplyfying, We have \textbf{$(x_2,y_2) = (9,-2)$}`