Final answer:
Using the midpoint formula to find the coordinates of point C and then applying the distance formula, the length of segment AC is approximately 7.21 units.
Step-by-step explanation:
To find the length of line segment AC, where point A is at (-2, 3), and the midpoint, point B, is at (0,6), we can use the midpoint formula to find the coordinates of point C. The midpoint formula states that the midpoint B's coordinates are the averages of the coordinates of points A and C. Therefore, we have:
Bx = (Ax + Cx) / 2 and By = (Ay + Cy) / 2
Substituting the given values for B and A, we get:
0 = (-2 + Cx) / 2 and 6 = (3 + Cy) / 2
Solving the equations for Cx and Cy gives us the coordinates of point C as (2, 9).
Now that we have the coordinates for points A (-2, 3) and C (2, 9), we can calculate the length of segment AC using the distance formula d = sqrt((Cx - Ax)^2 + (Cy - Ay)^2) which gives us a length of:
d = sqrt((2 - (-2))^2 + (9 - 3)^2) = sqrt((4)^2 + (6)^2) = sqrt(16 + 36) = sqrt(52) = 7.21 units (approximate to two decimal places).