Question 1091375
<br>Call the quadrilateral ABCD, with A(0,-1), B(-2,3), C(6,7), and D(8,3).  The quadrilateral is a rectangle if all the angles are right angles; the angles are right angles if adjacent sides are perpendicular to each other; adjacent sides are perpendicular to each other if their slopes are negative reciprocals.<br>
So find the slope of each side of the quadrilateral.  I think drawing a sketch is easier (and less prone to careless errors) than using the formula for the slope of a line segment between two points.<br>
The slope of AB is -2; the slope of BC is 1/2.  Since (-2)(1/2) = -1, AB and BC are perpendicular.<br>
Find the slopes of CD and DA to finish showing that the figure is a rectangle.