Question

In the diagram below of triangle JK L, M is the midpoint of J I and N is the midpoint of KL. If MN =

-52 + 31, and JK =
-8x + 52, what is the
measure of MN?

Answer 1

Based on the diagram provided, we can use the Midsegment Theorem, which states that the length of the segment connecting the midpoints of two sides of a triangle is half the length of the third side.

Since M is the midpoint of JI, we have MI = IJ. Similarly, since N is the midpoint of KL, we have KN = NL. Therefore, we can write:

JK = JI + IK

Since M is the midpoint of JI, we have:

JI = IM

Similarly, since N is the midpoint of KL, we have:

IK = KN

Therefore, we can rewrite the above equation as:

JK = IM + KN

Substituting the given values, we have:

-8x + 52 = (MN)/2

Multiplying both sides by 2, we get:

-16x + 104 = MN

Substituting the given value of MN, we have:

-16x + 104 = -21

Solving for x, we get:

x = -83/16

Therefore, the measure of MN is:

MN = -52 + 31 = -21