gprep -4 ps

abhasjha wrote:R, S, T, and U are points on a line, and U is the midpoint of line segment ST. If the lengths of line segments RS, RT, and ST are 20, 4, and 24, respectively. What is the length of line segment RU?

A. 6
B. 8
C. 12
D. 14
E. 16

Here's my step-by-step solution:

U is the midpoint of line segment ST, and the length of line segment ST is 24.
So, we get the following:


This means that SU and UT both have length 12:


The length of line segment RT is 4
There are two possible locations for R:
Case a:

In case a, the length of line segment SR is 28, but the question tells us that line segment SR has length 20.
So, R cannot be in the above location.

Case b:

In case b, the length of line segment SR is 20...PERFECT
Now that we've determined R's location, we can find the length of RU.


RU must have length 8

Answer: B

Cheers,
Brent