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<p>A kite is drawn with vertices at the top, right, bottom, and left. The upper left and right segments are congruent and short. The lower left and right segments are congruent and long. </p><p>The upper left segment is labeled y minus 4. <br/>The upper
Find the values of the variables in this kite.
To find the values of the variables in the kite, we can use the properties of a kite.
Let's label the vertices of the kite as follows:
- Top vertex: T
- Right vertex: R
- Bottom vertex: B
- Left vertex: L
Let's also label the lengths of the segments as follows:
- Upper left segment: x
- Upper right segment: x
- Lower left segment: y
- Lower right segment: y
Given the information provided, we have the following equations:
1. The upper left segment is labeled y minus 4: x = y - 4
2. The sum of the lengths of the diagonals is zero: x + y + x + y = 0 (diagonals intersect at the top vertex, forming a right angle)
We can solve this system of equations to find the values of x and y.
Simplify equation 2:
2x + 2y = 0
Divide both sides by 2:
x + y = 0
Now we have a system of two equations:
x = y - 4 (equation 1)
x + y = 0 (equation 3)
Substitute equation 3 into equation 1:
y - 4 + y = 0
Combine like terms:
2y - 4 = 0
Add 4 to both sides:
2y = 4
Divide both sides by 2:
y = 2
Now that we know the value of y, we can substitute it back into equation 1 to find the value of x:
x = y - 4
x = 2 - 4
x = -2
Therefore, the values of the variables in this kite are:
x = -2
y = 2