PQRS is a parallelogram
Step-by-step explanation:
In a parallelogram, opposite sides are parallel and congruent.
Applying the distance formula to determine if opposite sides are congruent will be;
Side PQ and SR
P(-6,4), Q (-2,7)
The distance formula for length of a segment given end points follows;
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute values in the equation
[tex]d=\sqrt{(-2--6)^2+(7-4)^2\\} \\d=\sqrt{4^2+3^2} =\sqrt{16+9} =\sqrt25} =5[/tex]
For side SR where S(-5,-3) and R(-1,0)
[tex]d=\sqrt{(-1--5)^2+(0--3)^2} \\\\d=\sqrt{(4^2+3^2} =\sqrt{16+9} =\sqrt{25} =5[/tex]
This shows side PQ is congruent to side SR
Checking congruent of side PS and QR
P(-6,4) ,S(-5,-3) ,Q(-2,7) and R(-1,0)
[tex]d=\sqrt{(-3-4)^2+(-5--6)^2} \\\\d=\sqrt{-7^2+1} =\sqrt{50}[/tex]
For QR
[tex]d=\sqrt{(-1--2)^2+(0-7)^2} \\\\d=\sqrt{1^2+-7^2} =\sqrt{1+49} =\sqrt{50}[/tex]
This shows side PS is congruent to side QR
Hence PQRS is a parallelogram
Learn More
Properties of a parallelogram :https://brainly.com/question/3100335
Keywords : vertices, quadrilateral , distance formula, slope formula
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