Question

If necessary, use "/" for the fraction bar. In triangle QPR with side QR equal to 8 units, X is the midpoint of side

QP, and a line falls from X to PRQ, the length of QR is 8 units. The length of mid-segment XY is ______ units.
a) 4
b) 8
c) 12
d) 16

Answer 1

The length of the mid-segment XY in triangle QPR is 4 units, according to the mid-segment theorem, which makes it half the length of side QR.

Step-by-step explanation:

In triangle QPR with side QR equal to 8 units. It is given that X is the midpoint of side QP, and XY is a mid-segment of the triangle that is parallel to side QR. The mid-segment theorem in geometry states that the mid-segment, which connects the midpoints of two sides of a triangle, will be parallel to the third side and half its length. Since QR is 8 units, mid-segment XY will be half of this length.

The length of mid-segment XY is therefore 8 units / 2, which equals 4 units.

The correct answer to the question would be option (a) 4.