SOLUTION: is the quadrilateral with the given vertices a parallelogram when using coordinate geometry? (1,4), (4,4), (5,1), (2,1)

Question 1137256: is the quadrilateral with the given vertices a parallelogram when using
coordinate geometry?
(1,4), (4,4), (5,1), (2,1)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
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answer: quadrilateral is a parallelogram, opposite sides are parallel and equal in length

Answer by ikleyn(52907)   (Show Source): You can put this solution on YOUR website!
.

The points (1,4) and (4,4) have equal y-coordinate y = 4, so they lie on the horizontal line parallel to x-axis.

The length of the side between these two pints is the difference of their x-coordinates 4 - 1 = 3.

The points (5,1) and (2,1) have equal y-coordinate y = 1, so they lie on the horizontal line parallel to x-axis.

The length of the side between these two pints is the difference of their x-coordinates 5 - 2 = 3.

So, the given quadrilateral has two the opposite sides parallel and of equal length.

It implies that the quadrilateral is a parallelogram.

See the lesson
    - Properties of the sides of parallelograms
in this site.

Also, you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lesson is the part of this textbook under the topic "Properties of parallelograms".

Save the link to this online textbook together with its description

Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson

to your archive and use it when it is needed.

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