Question

In parallelogram LMNO, MP = 21 m, LP = (y + 3) m, NP = (3y – 1) m, and
OP = (2x – 1) m.

Parallelogram L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P.

What are the values of x and y?

x = 10 m, y = 1 m
x = 10 m, y = 2 m
x = 11 m, y = 1 m
x = 11 m, y = 2 m

Answer 1

In a parallelogram the diagonals bisect each other, so MP = OP and LP = NP.

From MP = OP:
21 = 2x − 1 → 2x = 22 → x = 11.

From LP = NP:
y + 3 = 3y − 1 → 4 = 2y → y = 2.

So x = 11 m, y = 2 m (third option).