Answer:
Yes the Quadrilateral is a Parallelogram.
Step-by-step explanation:
A parallelogram can be defined as a quadrilateral i.e a geometric shape with four sides that has opposite sides parallel and equal in length.
From the question, we are given the following points
P(2, 2), Q(1, -3), R(-4, 2), S(-3, 7)
Given points: (x1, y1) and (x2, y2)
The formula would be
√(x2 - x1)² +(y2 - y1)²
a) P(2, 2), Q(1, -3)
Length PQ = √(1 - 2)² +(-3 - 2)² = √-1² + -5² = √26
b) R(-4, 2), S(-3, 7)
Length RS = √(-3 - (-4))² + (7 - 2) ² = √ 1² + 5² = √26
c) R(-4, 2), Q(1, -3)
Length RQ = √(1 - (-4))² + (-3 - 2)² = √5² + 5² = √(25 + 25) = √50
d) S(-3, 7), P(2, 2)
Length SP = √(2 - (-3))² + (2 - 7)² = √5² +(-5)² = √(25 + 25) = √50
From the above solution, we can see that
Length PQ = Length RS
Length RQ = Length SP
This means the opposite sides are parallel and equal in length, hence it is a Parallelogram.
