Question

When the coordinates (1, 1), (7, 3), (8, 0), and (2, −2) are joined, which shape is formed?

Answer 1

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:

$\text{Slope} = \frac{y_2-y_1}{x_2-x_1}$

Calculate the slope of each pairs:

For A(1, 1) and B(7, 3)

By definition of slope;

$\text{Slope of AB}= \frac{3-1}{7-1} = \frac{2}{6} = \frac{1}{3}$

Similarly,

For B(7, 3) and C(8, 0)

$\text{Slope of BC}= \frac{0-3}{8-7} = -\frac{3}{1} = -3$

For C(8, 0) and D(2, -2)

$\text{Slope of CD} = \frac{-2-0}{2-8} = \frac{-2}{-6} = \frac{1}{3}$

For D(2, -2) and A(1,1)

$\text{Slope of DA}= \frac{1-(-2)}{1-2} = -\frac{3}{1} = -3$

you can see that:

Slope of AB = Slope Slope of CD

and

Slope of BC = Slope of DA

Also;

$\text{Slope of AB} \times \text{Slope of BC} = -1$

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.

Answer 2

A rectangle that is tilted to the upper right is formed.