SOLUTION: is this quadrilateral, with the given vertices, a rectangle using coordinate geometry? A(4,1), B(0,7), C(-2,2), D(0,0)

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Question 1137258: is this quadrilateral, with the given vertices, a rectangle using coordinate
geometry?
A(4,1), B(0,7), C(-2,2), D(0,0)
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


To be a rectangle, we need...
opposite sides parallel;
opposite sides congruent;
adjacent sides perpendicular

Showing that ANY of those is not true means the quadrilateral is not a rectangle.

To show opposite sides parallel or adjacent sides perpendicular, we need to find slopes. To show opposite sides congruent, we only need to use the distance formula (aka Pythagorean Theorem); that seems easier.

And a quick look at the coordinates of the vertices shows that AB and CD are of different lengths.

So NO; the quadrilateral is not a rectangle.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

is this quadrilateral, with the given vertices, a rectangle using coordinate
geometry?
A(4,1), B(0,7), C(-2,2), D(0,0)
Diagonals of a rectangle are CONGRUENT.

BD and AC are diagonals of this quadrilateral

BD, having the same x-coordinates (0) has a length of 7 (7 - 0) and is actually located on the y-axis.

The other diagonal, AC, if calculated, using the distance formula is NOT 7 units long

As the diagonals are NOT CONGRUENT, this quadrilateral CANNOT be a rectangle. 

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