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Question

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.

(2 points)

Answer 1

Since DHEG is a parallelogram with diagonals that intersect at point H, we can use the properties of parallelograms to find the values of x and y.

In a parallelogram, opposite sides are equal. Therefore, we have the following equations:

DH = GH
x + 1 = 3x - 4

Simplifying the equation, we get:
2x = 5
x = 5/2

Now, let's look at the equation for the other pair of opposite sides:

HE = GF
5y + 1 = 3x + 4

Substitute the value of x we found:
5y + 1 = 3(5/2) + 4
5y + 1 = 15/2 + 8/2
5y + 1 = 23/2

Subtract 1 from both sides:
5y = 23/2 - 2/2
5y = 21/2

Divide both sides by 5:
y = (21/2) / 5
y = 21/10

Therefore, x = 5/2 and y = 21/10.