A quadrilateral has vertices with coordinates (-3,1), (0,3), (5,2), and (-1,-2). Which type of quadrilateral is this?

1 Answer
Daniel L.
Dec 6, 2017

It is a trapezoid. See explanation.

Explanation:

We can check what kind of quadrilateral is this by calculating slopes of its sides.

#m_{AB}=(y_B-y_A)/(x_B-x_A)#

#m_{AB}=(3-1)/(0-(-3))=2/3#

The same formula is used to calculate slopes of the remaining sides:

#m_{AD}=(-2-1)/(-1-(-3))=-3/2#

#m_{CD}=(-2-2)/(-1-5)=(-4)/-6=2/3#

#m_{BC}=(2-3)/(5-0)=-1/5#

From the above calculations we can see that:

#AB# and #DC# are parallel to each other, and both are perpendicular to #AD#. So the quadrilateral is a right angled trapezoid (#/_A# and #/_D# are right angles)

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