Use the image to answer the question.

Question

Points upper A upper C mark the ends of a line segment that slopes upward from left to right. Point upper B is at the midpoint. Identical single hash marks are between upper A and upper B and between upper B and upper C.

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

a. The measure of AC¯¯¯¯¯¯¯¯ is 11.15 millimeters.

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

c. The measure of AC¯¯¯¯¯¯¯¯ is 66.9 millimeters.

d. The measure of AC¯¯¯¯¯¯¯¯ is 44.6 millimeters.

Answer 1

To find the measure of \( AC \), we can follow the logic of the construction mentioned in the question.

1. Understanding the points:

   • \( A \) and \( C \) are the endpoints of the segment \( AC \).
   • \( B \) is the midpoint of segment \( AC \).

2. Given information:

   • The length of segment \( AB \) is 22.3 millimeters.
   • Since point \( B \) is the midpoint, this means that \( AB = BC \).

3. Calculating \( AC \):

   • The length of segment \( AC \) can be calculated as follows: \[ AC = AB + BC = AB + AB = 22.3 , \text{mm} + 22.3 , \text{mm} = 2 \times 22.3 , \text{mm} = 44.6 , \text{mm} \]

So, the measure of \( AC \) is 44.6 millimeters.

The correct response is: d. The measure of \( AC \) is 44.6 millimeters.