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The length of bar(WZ) is 3a+15, and the ...

The length of `bar(WZ)` is `3a+15`, and the length of `bar(WX)` is `7a+5`. If Y is the midpoint of `bar(XZ)`, what is the length of `bar(WY)` ?

A

`5+4a`

B

`5-2a`

C

`25+4a`

D

`10+5a`

Text Solution

Verified by Experts

The correct Answer is:
D
Usually the best thing to do to start on a plane geometry is to mark up the figure. Put as much of the information into the figure as you can. Doing so is a good way to organize your thoughts and avoid having to go back and forth between the figure and the question.

Now you can plan your attack. First subtract `bar(WX)` from the whole length `bar(WZ)` to get `bar(XZ)` :
`bar(XZ)=bar(WZ)-bar(WX)=(3a+15)-(7a+5)=3a+15-7a-5=-4a+10`
Then, because Y is the midpoint of `bar(XZ)`, you divide `bar(XZ)` by 2 to get `bar(XY)` and `bar(YZ)` :
`bar(XY)=bar(YZ)=(bar(XZ))/(2)=(-4a+10)/(2)=-2a+5`
Watch out ! That matches choice (B), but is not the final answer. What you're looking for is `bar(WY)`, so you have to add :
`bar(WY)=bar(WX)+bar(XY)=(7a+5)+(-2a+5)=5a+10`
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