Question

In the scenario where T is a segment bisector of XY at point M, and given that XM = 3x + 6 and MY = 2x + 14, what are the lengths of XM and MY respectively if x = 4?

A. XM = 18 and MY = 22
B. XM = 14 and MY = 22
C. XM = 18 and MY = 26
D. XM = 14 and MY = 26

Answer 1

Given that T bisects XY at M, making XM and MY equal and with the expressions for XM and MY, substituting x = 4 gives XM = 18 and MY = 22, which is answer choice A.

Step-by-step explanation:

When T is a segment bisector of XY at point M, it means that XM and MY are equal in length. Given the expressions XM = 3x + 6 and MY = 2x + 14, and knowing that XM = MY, we can set the two expressions equal to each other to find the value of x:

3x + 6 = 2x + 14

Solving for x gives us:

3x - 2x = 14 - 6

x = 8

However, the problem states that x = 4. So we substitute 4 back into both equations to find the actual lengths:

XM = 3(4) + 6 = 12 + 6 = 18

MY = 2(4) + 14 = 8 + 14 = 22

Therefore, the lengths of XM and MY when x = 4 are XM = 18 and MY = 22 respectively, which corresponds to answer choice A.