Question

Segment GT is a median of triangle UTS. Find if SU equals X - 9 and GU equals X - 10.

Option 1: If segment GT is a median, then GT equals X - 9.
Option 2: If segment GT is a median, then GT equals X - 10.
Option 3: If segment GT is a median, then GT equals (2X - 19)/2.
Option 4: If segment GT is a median, then GT equals (2X - 20)/2.

Answer 1

The correct length of the median GT in triangle UTS, when SU equals X - 9, is X - 9 regardless of the length of GU.

Step-by-step explanation:

The problem involves finding the length of the median of a triangle given certain algebraic expressions. In triangle UTS, segment GT is the median, which means it goes from vertex G to the midpoint of the opposite side US. If SU equals X - 9, then the midpoint of SU will also have this value, because a median divides the opposite side in half. Therefore, the median GT will not be affected by the length of GU, and the length of the median will only depend on the length of SU.

Given this information, the correct option is: Option 1: If segment GT is a median, then GT equals X - 9.

The other options are incorrect because the length of GU is irrelevant to the length of the median GT, and the expressions involving fractions do not apply to the explanation for a median in a triangle.