Below represents the proof that the quadrilateral QRST is a parallelogram
How to prove that QRST is a parallelogram?
The coordinates are given as:
Q = (-1,-1)
R = (2,9)
S = (-4,5)
T = (-7,-5)
Calculate the length of each side using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
So, we have:
[tex]QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}[/tex]
[tex]RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}[/tex]
[tex]ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}[/tex]
[tex]TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}[/tex]
The above computations show that opposite sides are equal.
Next, we determine the slope of each side using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]QR = \frac{9 + 1}{2 + 3} = \frac{10}3[/tex]
[tex]RS = \frac{5-9}{-4 - 2} = \frac{2}3[/tex]
[tex]ST = \frac{5+5}{-4 + 7} = \frac{10}3[/tex]
[tex]TQ = \frac{-5+1}{-7 + 1} = \frac{2}3[/tex]
The above computations show that opposite sides are parallel, because they have equal slope
Hence, the quadrilateral QRST is a parallelogram
Read more about parallelograms at:
https://brainly.com/question/3050890
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