Question

The vertices of quadrilateral PQRS are given below. Use the distance and/or slope formuals to determine is PQRS is a parallelogram. Use the diagram a a guide.

P(-6,4), 06-2, 7), R(-1,0), S(-5, -3)

P -------------------------- Q
/ /
/ /
S ------------------------- R

Answer 1

Since only one pair of opposite sides is parallel, PQRS is not a parallelogram.

Let's determine if PQRS is a parallelogram given the vertices of the quadrilateral.

We can use the distance formula and/or slope formula to determine if PQRS is a parallelogram. A parallelogram is a quadrilateral in which opposite sides are parallel and congruent.

1. Calculate the slopes of opposite sides:

Slope of PQ = (7 - 4) / (-6 - 0) = 3/6 = 1/2

Slope of RS = (-3 - 0) / (-5 - (-1)) = -3/4

Slope of PS = (4 - (-3)) / (-6 - (-5)) = 7/1

Slope of QR = (0 - 7) / (6 - (-1)) = -7/7 = -1

2. Check if opposite sides are parallel and congruent:

PQ is parallel to RS since their slopes are equal (1/2 = -1/2).

PS is not parallel to QR since their slopes are not equal (7/1 != -1).

PQ is not congruent to RS since their distances are not equal (√(49+1) != √(49+9)).