Answer:
The quadrilateral is not a parallelogram
Step-by-step explanation:
we know that
In a parallelogram opposite sides are parallel and congruent
Find the length of the sides of the quadrilateral
step 1
Find the distance QR
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
Q(-10,-2), R(1,-1)
substitute
[tex]d=\sqrt{(-1+2)^{2}+(1+10)^{2}}[/tex]
[tex]d=\sqrt{(1)^{2}+(11)^{2}}[/tex]
[tex]d=\sqrt{122}\ units[/tex]
step 2
Find the distance TS
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
T(-11,-8), S(1,-7)
substitute
[tex]d=\sqrt{(-7+8)^{2}+(1+11)^{2}}[/tex]
[tex]d=\sqrt{(1)^{2}+(12)^{2}}[/tex]
[tex]d=\sqrt{145}\ units[/tex]
we have that
QR and TS are opposite sides
In a parallelogram opposite sides are congruent but in this problem
[tex]QR \neq TS[/tex]
[tex]\sqrt{122}\ units \neq \sqrt{145}\ units[/tex]
therefore
The quadrilateral is not a parallelogram
