Question

If Y bisects XZ, find the value of x and the measure of the indicated segment.
5. XY = 7x + 6 and YZ = 2x + 21, find XY.
7x+62x+21
7x-2x = 21-6 X Y = 7/3) + 6 = 27
5x=
[x = 3
6. XY = 4x-8 and XZ = 14-2x, find XZ.
4x-8, 14-2x
(TURN OVER)
X
Y
XY = Yz
2

1. Applying the definition of a segment bisector, we have:
5. x = 3; XY = 27 units.
6. x = 3; XZ = 8 units.

### What is a Segment Bisector?

A segment bisector divides (bisects) a line segment into two parts that are congruent to each other.
We are told that Y bisects XZ, this means that, XY is congruent to YZ.
5. Given the following:
XY = 7x + 6
YZ = 2x + 21
Set both equal to each other and solve for x, since XY = YZ.
7x + 6 = 2x + 21
Combine like terms
7x – 2x = -6 + 21
5x = 15
5x/5 = 15/5
x = 3
XY = 7x + 6
XY = 7(3) + 6
XY = 21 + 6
XY = 27 units
6. XY = 4x – 8
XZ = 14 – 2x
XZ = 2(XY)
Plug in the values
14 – 2x = 2(4x – 8)
14 – 2x = 8x – 16
14 + 16 = 8x + 2x
30 = 10x
30/10 = x
x = 3
XZ = 2(4x – 8)
XZ = 2(4(3) – 8)
XZ = 8 units.