Question

In the figure, M and N are midpoints of RT and ST. What is the length of MN?
a + b
b - a
2

Answer 1

find M's and N's coordinates

Answer 2

then use the distance formula to find the length of MN

Answer 3

Theorem:
In a triangle, a segment that joins the midpoints of two sides is parallel to and half the length of the third side.

Answer 4

How would I find the coordinates?

Answer 5

find the midpoint of the RT for M
and find the midpoint of ST for N

use the midpoint formula (which is just take the average really)


like find the average of the x values of R and T
and
find the average of the y values of R and T


then you will do something similar for N's coordinates

Answer 6

okay, is my answer b-a?

Answer 7

looks good

Answer 8

also we could use @mathstudent55 's theorem
(well isn't his theorem but he wrote it)

the length of RS is 2b-2a=2(b-a)
and his theorem says that MN will be half that

Answer 9

okay, thank you so much!