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

The quadrilateral is not a parallelogram

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=√(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=√(145)\ units`

we have that

QR and TS are opposite sides

In a parallelogram opposite sides are congruent but in this problem

`QR \\eq TS`

`√(122)\ units \\eq √(145)\ units`

therefore

The quadrilateral is not a parallelogram