Question

Find the value of the variable and YZ if Y is between X and Z

XY=6b, YZ=8b, XZ=175

and can you show me how you got your answers

Answer 1

If point Y is between points X and Z, then

XY + YZ = XZ

In words, the distance from X to Y, plus the distance from Y to Z, is equal to the distance from X to Z. (See the attached picture.)

So 6b + 8b = 175

Can you finish it?

Answer 2

The value of b is 12.5. The length of YZ is 100 units.

Explanation:

Given information: XY=6b, YZ=8b, XZ=175 and Y is between X and Z.

It means X,Y, Z are collinear points and point Y divides the line segment XZ is two ports.

Using segment addition property, we get

`XY+YZ=XZ`

Substitute XY=6b, YZ=8b, XZ=175 in the above equation.

`6b+8b=175`

`14b=175`

Divide both sides by 14.

`b=(175)/(14)`

`b=12.5`

The value of b is 12.5.

The length of YZ is

`YZ=8b=8* 12.5=100`

Therefore the length of YZ is 100 units.