Question

after redesigning their logo, a company hired an artist to produce a copy of the new logo on the wall of their office lobby.
the artist took a transparency with the redesigned logo and used a projector to beam a copy, dilated by a scale factor of 10, onto the wall. after tracing the projected logo, the artist painted the tracing to produce a finished product.
which statement is true?

a. the painted logo is not similar to the version on the transparency because the corresponding side lengths have been made 10 units larger.

b. the painted logo is similar to the version on the transparency because the corresponding side lengths have been made 10 times as large.

c. the painted logo is similar to the version on the transparency because the corresponding side lengths have been made 10 units larger.

d. the painted logo is not similar to the version on the transparency because the corresponding side lengths have been made 10 times as large.

Explanation:

Step1: Recall Similar Figures Definition

Similar figures have corresponding angles equal and corresponding side lengths in proportion (scaled by a constant factor). Dilations (scaling) create similar figures as they preserve angle measures and scale sides by a constant.

Step2: Analyze the Dilation

The logo is dilated by a scale factor of 10. This means all corresponding side lengths of the painted logo (compared to the transparency) are 10 times as large. Since dilation preserves similarity (angles stay the same, sides are scaled proportionally), the painted logo is similar to the transparency version.

Step3: Evaluate Each Option

• Option A: Incorrect. Dilation (scale factor 10) creates similar figures. Side lengths are scaled by a factor, not "10 units larger" (units aren't specified, and dilation is a scale factor, not additive).
• Option B: Correct. Dilation by scale factor 10 means side lengths are 10 times as large, and dilation preserves similarity.
• Option C: Incorrect. Side lengths are scaled by a factor of 10 (multiplicative), not "10 units larger" (additive).
• Option D: Incorrect. Dilation (scaling by factor) creates similar figures, so they are similar.

Answer:

B. The painted logo is similar to the version on the transparency because the corresponding side lengths have been made 10 times as large.