Question

Rectangle DEFG is dilated with the origin as the center of dilation using the rule (x,y) --> (3,5x, 3.5y) to create rectangle D'EFGʻ. Which statement is true?

Rectangle D'EFG' is smaller than rectangle DEFG, because the scale factor is less than 1.
Rectangle D'EFG' is smaller than rectangle DEFG, because the scale factor is greater than 1.
Rectangle D'E'FG' is larger than rectangle DEFG, because the scale factor is greater than 1.
Rectangle D'EFG' is larger than rectangle DEFG, because the scale factor is less than 1.

Answer 1

We conclude that ''rectangle D'E'F'G' is larger than rectangle DEFG because the scale factor is greater than 1''.

Explanation:

We know that when an object is dilated by a scale factor, the shape of the original size does not change, but the size of the original object tends to change depending upon the value of a scale factor.

For example,

• If scale factor > 1, the image gets larges or stretched.

• If the scale is between 0 and 1, the image reduces.

• If the scale factor = 1, the figure and image will be congruent.

Given that Rectangle DEFG is dilated with the origin as the center of the dilation using the rule (x,y) --> (3.5x, 3.5y) to create rectangle D'E'F'G'.

Given the scale factor = 3.5

As the scale factor > 1

Thus, the rectangle D'E'F'G' is larger than the rectangle DEFG.

Therefore, we conclude that ''rectangle D'E'F'G' is larger than rectangle DEFG because the scale factor is greater than 1''.