In the diagram below of triangle J, K, LJKL, MM is the midpoint of start overline, J, L, end overline
JL
and NN is the midpoint of start overline, K, L, end overline
KL
. If M, N, equals, 2, x, plus, 13MN=2x+13, and J, K, equals, minus, 2, x, plus, 38JK=−2x+38, what is the measure of start overline, M, N, end overline
MN
?
Since M is the midpoint of JL, we can set up the equation:
2x + 13 = JK
And since N is the midpoint of KL, we can set up the equation:
2x + 13 = JK
Now we can set these two equations equal to each other:
JK = −2x + 38
2x + 13 = −2x + 38
Solving for x, we get:
4x = 25
x = 25/4
Now that we have found the value of x, we can substitute it back into one of the original equations to find the measure of MN:
MN = 2(25/4) + 13
MN = 25/2 + 13
MN = 12.5 + 13
MN = 25.5
Therefore, the measure of MN is 25.5.