Question

Points X and Z are on a number line, and point Y partitions

line XZ into two parts so that the ratio of the length of line

segment XY to the length of line segment YZ is 5:7. The

coordinate of X is 0.4, and the coordinate of Y is 5.8. What

is the coordinate of Z?

Answer 1

The coordinate of
`Z` is 13.36.

Explanation:

According to the statement, we have the following information:

`(XY)/(XZ) = (5)/(12)` (1)

`(YZ)/(XZ) = (7)/(12)` (2)

`X = 0.4` (3)

`Y = 5.8` (4)

From (2), we have the following expression:

`YZ = (7)/(12)\cdot XZ`

`Y-Z =(7)/(12)\cdot (X-Z)`

`Y - Z = (7)/(12)\cdot X -(7)/(12)\cdot Z`

`Y-(7)/(12)\cdot X = Z-(7)/(12)\cdot Z`

`(5)/(12)\cdot Z = Y-(7)/(12)\cdot X`

`5\cdot Z = 12\cdot Y-7\cdot X`

`Z = (12)/(5)\cdot Y-(7)/(5)\cdot X` (5)

If we know that
`Y = 5.8` and
`X = 0.4`, then the coordinate of
`Z` is:

`Z = (12)/(5)\cdot (5.8)-(7)/(5)\cdot (0.4)`

`Z = 13.36`

The coordinate of
`Z` is 13.36.