Nozomi constructed a copy of AB¯¯¯¯¯¯¯¯ by using point B as an endpoint of the copy of AB¯¯¯¯¯¯¯¯ and placing point C, as seen in the image. If the measure of AB¯¯¯¯¯¯¯¯ is 22.3 millimeters, what is the measure of AC¯¯¯¯¯¯¯¯?

Question

Nozomi constructed a copy of AB¯¯¯¯¯¯¯¯ by using point B as an endpoint of the copy of AB¯¯¯¯¯¯¯¯ and placing point C, as seen in the image. If the measure of AB¯¯¯¯¯¯¯¯ is 22.3 millimeters, what is the measure of AC¯¯¯¯¯¯¯¯?

(1 point)
Responses

The measure of AC¯¯¯¯¯¯¯¯ is 66.9 millimeters.
The measure of  Modifying above upper A upper C with bar  is 66.9 millimeters.

The measure of AC¯¯¯¯¯¯¯¯ is 11.15 millimeters.
The measure of  Modifying above upper A upper C with bar  is 11.15 millimeters.

The measure of AC¯¯¯¯¯¯¯¯ is 44.6 millimeters.
The measure of  Modifying above upper A upper C with bar  is 44.6 millimeters.

The measure of AC¯¯¯¯¯¯¯¯ is 22.3 millimeters.

GPT-4o mini · Answer

To determine the measure of $ \overline{AC} $, we first need to understand how Nozomi constructed $ \overline{AC} $. It was mentioned that point $ B $ is used as an endpoint for the copy of $ \overline{AB} $, meaning that $ \overline{AC} $ extends from point $ A $ to point $ C $ with $ C $ being the new point created by this operation. Since $ \overline{AB} $ has a measure of 22.3 millimeters, and $ \overline{AC} $ is formed by extending this segment continuously using $ B $ as a new endpoint, we can deduce the length of $ \overline{AC} $. Assuming $ \overline{AC} $ is formed by placing another segment equal to $ \overline{AB} $ after point $ B $, the total length would be: $$ AC = AB + BC $$ Here, since $ BC $ is also a copy of $ \overline{AB} $, then: $$ BC = 22.3 \text{ millimeters} $$ Thus, the total length would be: $$ AC = 22.3 + 22.3 = 44.6 \text{ millimeters} $$ Therefore, the measure of $ \overline{AC} $ is **44.6 millimeters**. The correct response is: - The measure of $ \overline{AC} $ is 44.6 millimeters.