Question

What is the length of segment AC?

On a coordinate plane, line A C has points (3, negative 1) and (negative 5, 5).

Answer 1

To find the length of segment AC between the points \( A(3, -1) \) and \( C(-5, 5) \), we can use the distance formula:

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

In this case, we have:
- \( (x_1, y_1) = (3, -1) \)
- \( (x_2, y_2) = (-5, 5) \)

Now, we can plug the coordinates into the formula:

\[
d = \sqrt{((-5) - 3)^2 + (5 - (-1))^2}
\]

Now, calculate the differences:

\[
x_2 - x_1 = -5 - 3 = -8
\]
\[
y_2 - y_1 = 5 - (-1) = 5 + 1 = 6
\]

Now, substitute these differences back into the distance formula:

\[
d = \sqrt{(-8)^2 + (6)^2}
\]

Calculating the squares:

\[
(-8)^2 = 64
\]
\[
(6)^2 = 36
\]

Now, add these values:

\[
d = \sqrt{64 + 36}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]

Thus, the length of segment AC is \( \boxed{10} \).