Given:AB = 4x + 9 and DC = 6x − 5 Find:MN in terms of x

Question

The drawing shows trapezoid ABCD with AB ∥ DC;

 also, M and N are midpoints of AD and BC,

 respectively.

Trapezoid A B C D has four labeled vertices, two labeled points, and a line segment.

1. The top side is horizontal, starts at vertex A on the left and ends at vertex B on the right.
2. The right side starts at vertex B, goes down and to the right and ends at vertex C.
3. The bottom side is horizontal, starts at vertex C on the right and ends at vertex D on the left.
4. The left side starts at vertex D, goes up and to the right and ends at vertex A.
5. Point M is on side A D and point N is on side B C.
6. A horizontal line segment connects point M to point N.

Given:AB = 4x + 9 and DC = 6x − 5

Find:MN in terms of x

Answer 1

Length of line connecting midpoint of a trapezoid is equal to the average of the lengths of the two bases.

MN = (AB + DC) / 2

(4x + 9 + 6x - 5)/2 = (10x + 4)/2 = 5x + 2