How does scale factor change the area?

in summary, a scale factor is simply a number that multiplies the dimensions of a shape. ... If the scale factor is three, then the perimeter of the new object will be three times the original perimeter. The area of a scaled object will be equal to the scale factor squared.

Step-by-step explanation:

For example, if you had a triangle with a base measuring 6 units, and a height measuring 3 units, the area would be 9 square units. If we scale it by 1/3, the triangle's base is 2 units, the height is 1 unit, and the area is 1 square unit. The dimensions were scaled by 1/3, but the area was scaled by 1/9 (1/3 * 1/3).

We have been given a transformation having rule

(x, y) → (x, 2y) on the parallelogram ABCD whose vertices are:

A(0, 0), B(1, 1), C(3, 1), and D(2, 0).

In given transformation x is same on both sides so x-coordinate will not change.

y changes to 2y so y-coordinate doubles. Due to that change in y, side length of the parallelogram will  change. Also the angle will change as you can see in the picture.

Now we can easily select True or False for each statement.

"The transformation preserves parallelism."

True

"The transformation preserves distance."

False

"The transformation preserves angle measure."

False