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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

Respuesta :

akposevictor

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.

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