oints K, L, and M are the midpoints of their respective sides. Given that the measure of ML is represented by the expression 4x – 13, and the measure of YX is represented by the expression 3x + 9, determine the value of x.

According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."

How to solve the question?

In the question, we are given that points K, L, and M, are the midpoints of their respective sides.

We are asked to determine the value of x, given that the measure of ML is represented by the expression 4x – 13, and the measure of YX is represented by the expression 3x + 9.

By midpoint theorem, we know that since M and L are midpoints of their respective sides, the line segment ML is parallel to the line segment YX, and ML is half of YX.

Thus, we get an equation,

ML = (1/2) of YX,

or, 2ML = YX.

Putting in the expressions for ML and YX, we get:

2(4x - 13) = 3x + 9,

or, 8x - 26 = 3x + 9,

or, 8x - 3x = 9 + 26,

or, 5x = 35,

or, x = 7.

Thus, the value of x is 7. Computed using the midpoint theorem.

Learn more about the mid-point theorem of the triangle at

https://brainly.com/question/9635025

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For the diagram refer to the attachment.