Use the image to answer the 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

The measure of AC¯¯
is 22.3 millimeters.
The measure of Modifying above upper A upper C with bar is 22.3 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 66.9 millimeters.

1 answer

To find the measure of \( \overline{AC} \), we need to analyze the information given.

The segment \( \overline{AB} \) is given as 22.3 millimeters, and point \( B \) is the midpoint of line segment \( \overline{AC} \). Since \( B \) is the midpoint, it divides \( \overline{AC} \) into two equal parts: \( \overline{AB} \) and \( \overline{BC} \).

Therefore, the length of \( \overline{AB} \) is equal to the length of \( \overline{BC} \): \[ AB = BC = 22.3 , \text{mm} \]

The total length of \( \overline{AC} \) can be calculated as: \[ AC = AB + BC = 22.3 , \text{mm} + 22.3 , \text{mm} = 44.6 , \text{mm} \]

Thus, the measure of \( \overline{AC} \) is 44.6 millimeters.

The correct response is: The measure of \( \overline{AC} \) is 44.6 millimeters.