Question

Ys is the perpendicular bisector of xz. What is the length of Xs if xz is 18 inches long?

Answer 1

XS is 9 inches long.

Explanation:

Given that

YS is the perpendicular bisector of XZ.

Length of XZ = 18 inches

To find:

Length of XS = ?

Solution:

First of all, let us learn about the perpendicular bisector.

Perpendicular bisector of a line AB is a line PQ, which divides the line AB in two equal parts and is at an angle of
`90^\circ` with the line AB.

If B is on the line PQ, then
`BP = BQ = (PQ)/(2)` and

`\angle ABP = \angle ABQ = 90^\circ`

Applying the above property in our given question.

Kindly refer to the attached image for the given dimensions.

S is on the line XZ.

`XS = SZ = (XY)/(2) = (18)/(2) \\\Rightarrow \bold{XS = 9\ inches}`

So, the answer is XS is 9 inches long.