Question

The vertices of quadrilateral PQRS are P(-6, 4)Q(-27)R(-1, 0)S(-5, -3)Use the distance and/or slope formula to determine if PQRS is a parallelogramUse the diagram as a guide.

Answer 1

Explanation:

Step 1: To determine if quadrilateral PQRS is a parallelogram, we must check if its opposite sides are both parallel and congruent.

Step 2: To check if the opposite sides are parallel, we can use the slope formula to calculate the slope of each side:

Slope of line PQ: m = (y2-y1)/(x2-x1)

m = (4-(-27))/(-6-(-27))

m = 31/-21

m = -1.476

Slope of line RS: m = (y2-y1)/(x2-x1)

m = (0-(-3))/(-1-(-5))

m = 3/-4

m = -0.75

Step 3: Since the slopes of PQ and RS are the same, they are parallel.

Step 4: To check if the sides are congruent (equal in length), we can use the distance formula:

Distance between P and Q: d = √((x2-x1)^2+(y2-y1)^2)

d = √((-27-(-6))^2+(4-(-27))^2)

d = √587

d = 24.25

Distance between R and S: d = √((x2-x1)^2+(y2-y1)^2)

d = √((-1-(-5))^2+(0-(-3))^2)

d = √26

d = 5.1

Step 5: Since the lengths of the opposite sides are not equal, the sides are not congruent.

Therefore, quadrilateral PQRS is not a parallelogram.