Question

The points A(-2, 4) and B(-2, -2) are plotted on the coordinate plane shown. a. Plot and label points C, D, E, and F so that squares ABCD and ABEF are formed. b. Determine the area of each square. c. Compare your squares with your classmates' squares. Are all the squares the same or different? How do you know that the squares are drawn correctly?

Answer 1

The labelled plotting of points C, D, E, and F so that squares ABCD and ABEF are formed is attached

The calculated areas of the squares are 36 square units

Plotting and labelng points C, D, E, and F so that squares ABCD and ABEF are formed

From the question, we have the following parameters that can be used in our computation:

A (-2, 4) and B (-2, -2)

For the squares ABCD and ABEF to be formed, we start by calculating the side length AB using

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

So, we have

AB = √[(-2 + 2)² + (4 + 2)²] = 6

This means that the side length AB is 6 and as such the squares ABCD and ABEF must have a side length of 6

So, we have the coordinates of C, D, E and F to be

C = (-2 + 6, 4) = (4, 4)

B = (-2 + 6, -2) = (4, -2)

E = (-2 - 6, 4) = (-8, 4)

F = (-2 +-6, -2) = (-8, -2)

Hence, the shapes are attached

Next, we have the areas to be

Area = Side length * Side length

This gives

Area = 6 * 6

Evaluate

Area = 36

Hence, the areas of the squares are 36 square units