Since DEFG is a parallelogram, its diagonals DE and FG bisect each other. Therefore, DH = HG and HF = HE.
From the given information, we have:
DH = x + 1 (1)
HF = 3y (2)
GH = 3x - 4 (3)
HE = 5y + 1 (4)
Since DH = HG, we can equate equations (1) and (3):
x + 1 = 3x - 4
4 = 2x
x = 2
Replacing x = 2 in equation (3):
GH = 3(2) - 4
GH = 6 - 4
GH = 2
Since HF = HE, we can equate equations (2) and (4):
3y = 5y + 1
-2y = 1
y = -1/2
Therefore, the values of x and y are x = 2 and y = -1/2.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The figure is parallelogram D E F G with diagonals that intersect at point H
In parallelogram DEFG, DH = x + 1, HF = 3y, GH = 3x − 4,
and HE = 5y + 1. Find the values of x and y. The diagram is not drawn to scale.
1 answer