P(2, 2), Q(1, -3), R(-4, 2), S(-3, 7) Using the information above, answer the following questions. Find the length of RS Find the length of SP Find the length of PQ Find the length of RQ Use this information to determine if the quadrilateral a parallelogram.

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.

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this