Question

Please help me with the question in the picture

Answer 1

XZ = 7.5

Explanation:

A drawing is sometimes very helpful.

Start by drawing a segment with endpoints W and Z.

+--------------------------------------------+

W Z

Y is the midpoint of WZ. Draw point Y in between W and Z and the same distance from both W and Z.

+---------------------+--------------------+

W Y Z

X is the midpoint of WY. Draw X between W and Y, and the same distance to W and Y.

+----------+----------+--------------------+

W X Y Z

Because of the midpoints, we know that:

WX = XY

WY = YZ

WY = 5

WX and XY are each half of WY, so WX = XY = 5/2 = 2.5

WY = YZ = 5

XZ = XY + YZ

XZ = 2.5 + 5

XZ = 7.5

Answer 2

7.5

Explanation:

W -- X -- Y ----- Z

We are given that :

• Y is the midpoint of WZ meaning that WY = YZ
• X is the midpoint of WY meaning that WX = XY
• WY = 5

Given this we want to find XZ

XZ consists of XY and YZ so we must find the length of the individual segments.

Finding YZ

Here, we know that YZ = WY as y is the midpoint of WZ. If WY = 5 then YZ also = 5

Finding XY

Given that WY = 5 and that X is a midpoint of WY we know that the segments WX and XY = WY and are congruent.
In other words we can say that 2XY = WY

==> WY = 5

2XY = 5

==> divide both sides by 2

XY = 2.5

Finding XZ

Again, XY + YZ = XZ

We have XY = 2.5 and YZ = 5

Hence, 2.5 + 5 = XZ

XZ = 7.5