Question

Identify the segment bisector of XY.

Answer 1

Given the image attached, the segment bisector that divides XY into two and the length of XY are as follows:

• Segment bisector of XY = line n
• Length of XY = 6

Recall:

• A line that divides a segment into two equal parts is referred to as segment bisector.

In the diagram attached below, line n divides XY into XM and MY.

Thus, the segment bisector of XY is: line n.

Find the value of x:

XM = MY (congruent segments)

• Substitute

$5x + 8 = 9x + 12$

• Collect like terms and solve for x

$5x + 8 = 9x + 12\\5x - 9x = -8 + 12\\\\-4x = 4\\\\x = -1$

XY = XM + MY

$XY = 5x + 8 + 9x + 12$

• Plug in the value of x

$XY = 5(-1) + 8 + 9(-1) + 12\\\\XY = -5 + 8 -9 + 12\\\\\mathbf{XY = 6}$

Therefore, given the image attached, the segment bisector that divides XY into two and the length of XY are as follows:

• Segment bisector of XY = line n
• Length of XY = 6

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