A figure is located at (2.0), (2-2). (6.-2), and (6.0) on a coordinate plane. What kind of 3-D shape would be created if the figure was rotated around the x-axis? provide an explanation and proof of your answer to receive full credit. Include the dimensions of the 3-D shape in your explanation

The shape created if the shape is rotated about the x-axis is the shape of a cylinder

Step-by-step explanation:

The (vertices) coordinates of the figure are; (2, 0), (2, -2), (6, -2), and (6, 0), we represent the figure as ABCD as follows;

A(2, 0), B(2, -2), C(6, -2), and D(6, 0)

We note that points with the same x-coordinate are on the same vertical line while points having the same y-coordinates are on the same horizontal line;

Therefore, we have;

The line AB = A vertical line segment

The line CD = A vertical line segment

The line BC = A horizontal line segment

The line AD = A horizontal line segment

The figure ABCD is therefore has 2 pairs of parallel lines (1 pair of vertical lines and 1 pair of horizontal line) with the lines perpendicular to each other, therefore, the interior angles of the line are 90° each

The figure ABCB to be rotated is therefore a rectangle with the top edge on the x-axis

The formula for the rotation of a figure is given as follows;

Where;

y = Constant = The radius of the 3-D volume created by the rotation, r

(a - b) = The length of the figure, l

Plugging in 'r', and 'y' in the above equation for 'V', gives;

Therefore, the volume created by the rotation of the figure, 'V', is the volume of a cylinder, and therefore, the shape created if the shape is rotated about the x-axis is a cylinder

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis