The length of the line segment XY which was bisected at point M is;
1) 32
2) 6
How to solve division of line segments?
1) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;
XM = YM and XM + YM = XY
We are given that;
XM = 3x + 1
YM = 8x - 24
Thus;
3x + 1 = 8x - 24
8x - 3x = 1 + 24
5x = 25
x = 25/5
x = 5
Thus;
XM = 3(5) + 1 = 16
YM = 8(5) - 24 = 16
XY = 16 + 16 = 32
2) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;
XM = YM and XM + YM = XY
We are given that;
XM = 5x + 8
YM = 9x + 12
Thus;
5x + 8 = 9x + 12
9x - 5x = 8 - 12
4x = -4
x = -1
XM = 5(-1) + 8 = 3
YM = 9(-1) + 12 = 3
XY = 6
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