Question

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

Answer 1

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

Answer 2

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} = (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}= (3-1)/(7-1) = (2)/(6) = (1)/(3)`

Similarly,

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

`\text{Slope of BC}= (0-3)/(8-7) = -(3)/(1) = -3`

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

`\text{Slope of CD} = (-2-0)/(2-8) = (-2)/(-6) = (1)/(3)`

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

`\text{Slope of DA}= (1-(-2))/(1-2) = -(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} * \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.