Question

The diagram shows quadrilateral MNPQ.

Quadrilateral M N P Q is shown. Sides N P and M Q are parallel. Angles P and Q are right angles. The length of M N is 10, the length of N P is 3, and the length of P Q is 6.

What is the length of line segment MQ?

8 units
10 units
11 units
15 units

Answer 1

Place P at (0,0) and PQ along the x-axis, so Q = (6,0). Since ∠P and ∠Q are right angles, NP and MQ are both vertical; with NP = 3, take N = (0,3) and M = (6,h).
MN = 10 gives sqrt[(6-0)^2 + (h-3)^2] = 10 → 36 + (h-3)^2 = 100 → (h-3)^2 = 64 → h = 11 (positive choice).
Thus MQ = distance from Q(6,0) to M(6,11) = 11 units.

Answer: 11 units.