Question

If three coordinates of a quadrilateral composed in the first quadrant t the coordinate plane are (0,0), (a,b), (a+c,b) and (c,o), which is the most accurate classification of the quadrilateral?

Answer 1

Let
P = (0,0)
Q = (a,b)
R = (a+c,b)
S = (c,0)
be four points of this quadrilateral. Let's find the slopes of each side

Slope of PQ = (y2-y1)/(x2-x1)
Slope of PQ = (b-0)/(a-0)
Slope of PQ = b/a

Slope of QR = (y2-y1)/(x2-x1)
Slope of QR = (b-b)/(a+c-a)
Slope of QR = (0)/(c)
Slope of QR = 0

Slope of RS = (y2-y1)/(x2-x1)
Slope of RS = (0-b)/(c-(a+c))
Slope of RS = (-b)/(c-a-c)
Slope of RS = (-b)/(-a)
Slope of RS = b/a

Slope of SP = (y2-y1)/(x2-x1)
Slope of SP = (0-0)/(c-0)
Slope of SP = 0/c
Slope of SP = 0

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Hopefully you can see how:

Slope of PQ = Slope of RS = b/a
Slope of QR = Slope of SP = 0

Effectively telling us that the opposite sides are parallel (recall that parallel lines have equal slopes).

The opposite sides are parallel, so this quadrilateral is a parallelogram

Final Answer: Parallelogram