We were given the following points;
A(4,6), B(6,10), C(0,13) , D(-2,9).
Slope of AB = (10-6)/(6-4)
= 4/2
=2
Slope of CD = (13-9)/(0--2)
= 4/2
=2
Slope of AD = (9-6)/(-2-4)
= 3/-6
= -½
Slope of BC = (13-10)/(0-6)
= 3/-6
= - ½
Slope of AB = slope of DC= 2
This tells us that side AB and DC of the quadrilateral are parallel.
Also
Slope of AD = slope of BC= - ½
This tells us that side AD and BC of the quadrilateral are also parallel.
Again;
Slope of AB × AD = 2 × - ½ = -1
This tells us that AB is perpendicular to AD.
Similarly;
Slope of AB × BC = 2 × - ½ = -1
This tells us that AB is perpendicular to BC.
The same thing applies to BC and CD, CD an AD.
The quadrilateral is therefore a rectangle.