Question

Determine the length of AC. (1 point) Responses 3.61 3.61 7.81 7.81 6.32 6.32 5
A is at -3,3
C is at 1,6

Answer 1

To determine the length of the segment AC, we can use the distance formula. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

In this case, point A is at \((-3, 3)\) and point C is at \((1, 6)\).

Let’s plug in these coordinates into the formula:

1. \(x_1 = -3\), \(y_1 = 3\)
2. \(x_2 = 1\), \(y_2 = 6\)

Now substituting these values into the distance formula:

\[
d = \sqrt{(1 - (-3))^2 + (6 - 3)^2}
\]
\[
= \sqrt{(1 + 3)^2 + (3)^2}
\]
\[
= \sqrt{(4)^2 + (3)^2}
\]
\[
= \sqrt{16 + 9}
\]
\[
= \sqrt{25}
\]
\[
= 5
\]

Therefore, the length of AC is **5**.