Question

Determine whether the quadrilateral is a parallelogram using the indicated method Q(-10,-2), R(1,-1), S(1,-7), T(-11,-8) (Distance Formula
)

Answer 1

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

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

Q(-10,-2), R(1,-1)

substitute

$d=\sqrt{(-1+2)^{2}+(1+10)^{2}}$

$d=\sqrt{(1)^{2}+(11)^{2}}$

$d=\sqrt{122}\ units$

step 2

Find the distance TS

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

T(-11,-8), S(1,-7)

substitute

$d=\sqrt{(-7+8)^{2}+(1+11)^{2}}$

$d=\sqrt{(1)^{2}+(12)^{2}}$

$d=\sqrt{145}\ units$

we have that

QR and TS are opposite sides

In a parallelogram opposite sides are congruent but in this problem

$QR \neq TS$

$\sqrt{122}\ units \neq \sqrt{145}\ units$

therefore

The quadrilateral is not a parallelogram