Question

Determine the length of AC
A (-3,3)
C (1,6)

Answer 1

To find the length of line segment \( AC \) between the points \( A(-3, 3) \) and \( C(1, 6) \), we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( C \):
- \( A(-3, 3) \) implies \( x_1 = -3 \) and \( y_1 = 3 \)
- \( C(1, 6) \) implies \( x_2 = 1 \) and \( y_2 = 6 \)

Now we can plug in these values into the distance formula:

\[
d = \sqrt{(1 - (-3))^2 + (6 - 3)^2}
\]

Calculating the differences:

\[
1 - (-3) = 1 + 3 = 4
\]
\[
6 - 3 = 3
\]

Now substitute the differences back into the equation:

\[
d = \sqrt{(4)^2 + (3)^2}
\]

Calculating the squares:

\[
d = \sqrt{16 + 9}
\]

Now add them together:

\[
d = \sqrt{25}
\]

Finally, take the square root:

\[
d = 5
\]

Thus, the length of segment \( AC \) is \( \boxed{5} \).