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

x = 11 m, y = 2 m ⇒ D

Step-by-step explanation:

In the parallelogram, diagonals bisect each other

∵ LMNO is a parallelogram

∵ OM and LN are its diagonals

∵ OM ∩ LN at point P

→ By using the fact above

∴ P is the mid-point of OM and LN

∴ OP = MP and LP = NP

∵ OP = MP

∵ OP = 2x - 1

∵ MP = 21

∴ 2x - 1 = 21

→ Add 1 to both sides

∴ 2x = 22

→ Divide both sides by 2

∴ x = 11 m

∵ LP = NP

∵ LP = y + 3

∵ NP = 3y - 1

∴ y + 3 = 3y -1

→ Add 1 to both sides

∴ y + 4 = 3y

→ Subtract y from both sides

∴ 4 = 2y

→ Divide both sides by 2

∴ 2 = y

∴ y = 2 m