Question

The points Q, left parenthesis, minus, 4, comma, minus, 5, right parenthesis, comma, R, left parenthesis, 8, comma, minus, 8, right parenthesis, comma, S, left parenthesis, 9, comma, minus, 4, right parenthesisQ(−4,−5),R(8,−8),S(9,−4), and T, left parenthesis, minus, 3, comma, minus, 1, right parenthesisT(−3,−1) form quadrilateral QRST. Plot the points then click the "Graph Quadrilateral" button., On this question page, you will first graph points on a coordinate grid. Following the graph are two buttons, "Graph Quadrilateral" will drawn lines between your points, and "Reset" will remove all of your points. Once you press Graph Quadrilateral, if your points are correct, the answer area will appear.
Click on the graph to plot a point. Click a point to delete it.
x
y
Q
R
S
T
Use the dropdown menus and answer blanks below to prove the quadrilateral is a rectangle.
Answer
Attempt 1 out of 2

I will prove that quadrilateral QRST is a rectangle by demonstrating that
both pairs of opposite sides are parallel
.
slope of QR =
slope of RS =
slope of ST =
slope of TQ =
The slopes of any pair of
sides are
.
That being the case, those sides are
.
Therefore the quadrilateral is a
.

Answer 1

slope of QR = -1/4
slope of RS = 4
slope of ST = -1/4
slope of TQ = 4

The slopes of any pair of opposite sides are equal.
That being the case, those sides are parallel.
Therefore the quadrilateral is a parallelogram.

Additionally, slope(QR) · slope(RS) = (-1/4)·4 = -1, so QR ⟂ RS. A parallelogram with one right angle is a rectangle. Hence QRST is a rectangle.