Question

What special type of quadrilateral has the vertices M(3,4), N(1,-6), P(6,-7), and Q(8,3)?
Answer square
rhombus

rectangle
trapezoid

Answer 1

Looking at the slopes we get the following:

MQ -> -1/5
QP -> 5
NP -> -1/5
MN -> 5

So, since opposite sides have the same slope they are parallel. That can rule out trapezoid.

Also, adjacent slopes are negative reciprocals. That means the angles are right. That rules out rhombus.

All that's let is to see if adjacent sides are equal in length.

Check the distance from MN and compare it to the distance from MQ and see if they are equal.

If they are, it's a square, if not, it's a rectangle.