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)
[tex]5x + 8 = 9x + 12[/tex]
- Collect like terms and solve for x
[tex]5x + 8 = 9x + 12\\5x - 9x = -8 + 12\\\\-4x = 4\\\\x = -1[/tex]
XY = XM + MY
[tex]XY = 5x + 8 + 9x + 12[/tex]
[tex]XY = 5(-1) + 8 + 9(-1) + 12\\\\XY = -5 + 8 -9 + 12\\\\\mathbf{XY = 6}[/tex]
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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