Answer:
Rectangle states that a parallelogram all of whose interior angles are right angle i.e, 90 degree and opposite sides are equal.
Given the coordinates
A(1, 1) , B(7, 3) , C(8, 0) and D(2, -2)
Using Slope formula:
[tex]\text{Slope} = \frac{y_2-y_1}{x_2-x_1}[/tex]
Calculate the slope of each pairs:
For A(1, 1) and B(7, 3)
By definition of slope;
[tex]\text{Slope of AB}= \frac{3-1}{7-1} = \frac{2}{6} = \frac{1}{3}[/tex]
Similarly,
For B(7, 3) and C(8, 0)
[tex]\text{Slope of BC}= \frac{0-3}{8-7} = -\frac{3}{1} = -3[/tex]
For C(8, 0) and D(2, -2)
[tex]\text{Slope of CD} = \frac{-2-0}{2-8} = \frac{-2}{-6} = \frac{1}{3}[/tex]
For D(2, -2) and A(1,1)
[tex]\text{Slope of DA}= \frac{1-(-2)}{1-2} = -\frac{3}{1} = -3[/tex]
you can see that:
Slope of AB = Slope Slope of CD
and
Slope of BC = Slope of DA
Also;
[tex]\text{Slope of AB} \times \text{Slope of BC} = -1[/tex]
Similarly, the product of slope of all pairs of consecutive sides are perpendicular( i.e, 90 degree).
Then by definition of Rectangle;
when the coordinates (1, 1), (7, 3), (8, 0), and (2, −2) are joined then, the shape Rectangle is formed.
