Question

Classify PQRS with coordinates P (3,7), Q (-1,7), R (3, -1) and S (-1, -1) using as many terms as possible.

Answer 1

Rectangle

Explanation:

The given quadrilateral has coordinates at: P (3,7), Q (-1,7), R (3, -1) and S (-1, -1).

The length of PQ is given by:

`|PQ|=|3--1|=|4|=4`

The length of QS is
`|QS|=|7--1|=|8|=8`

The length of RS is
`|RS|=|3--1|=|4|=4`

The length of PR is
`|PR|=|7--1|=|8|=8`

The slope of PQ is
`(7-7)/(3--1)=0`

The slope of QS is
`(-1-7)/(-1+1)= \infty`

The slope of RS
`(-1--1)/(-1-3) =0`

The slope of PR is
`(-1-7)/(3-3)=\infty`

The quadrilateral has pair of parallel sides equal and adjacent sides perpendicular.

This is a rectangle