Does the name correctly describe the shape given by the points A(2, 2), B(3, 4) , C(6, 4) , and D(5, 2)? Rectangle,Parallelogram,Square (yes or no)

Answer 1

If you plot the points on a coordinate plane, the quadrilateral sure looks like a parallelogram. But could it be a rectangle, square, or even a rhombus?

To be sure calculate the slope of each line segment. If opposite sides have the same slope, then opposite sides are parallel, which means indeed a parallelogram. That proves to be the case.

If the slopes of adjacent sides happen to be negative reciprocals (like 2 and -1/2 for example), then the quadrilateral is a rectangle; (not the case).and therefore not a square.

Finally if rhombus was one of your choices you would need to find the length of each side to determine if all sides have the same length.

Here is a link showing the calculations:

desmos.com/calculator/umoty91tdb

Answer 2

So let's start by graphing those four points. I did so on wolfram alpha (desmos is another option):

https://www.wolframalpha.com/input/?i=+plot+%282%2C+2%29%2C+%283%2C+4%29+%2C+%286%2C+4%29+%2C+%285%2C+2%29

As you can see if you go to the link, we have four points that form two sets of parallel points that are not perpendicular to each other.

Since the two sets of lines are not perpendicular and do not form right angles, this shape cannot be a square nor can it be a rectangle. (Both squares and rectangles are equiangular, meaning they have all four angles being the same at 90 degrees).

However, since both sets of opposites are parallel and equal, this is indeed a parallelogram.