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To find the length of side \( AC \) of triangle \( ABC \), we can use the distance formula, which is given by:

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

In this case:
- The coordinates of point \( A \) are \( (-2, 0) \),
- The coordinates of point \( C \) are \( (4, 3) \).

Now we can plug these values into the distance formula:

\[
AC = \sqrt{(4 - (-2))^2 + (3 - 0)^2}
\]
\[
AC = \sqrt{(4 + 2)^2 + 3^2}
\]
\[
AC = \sqrt{6^2 + 3^2}
\]
\[
AC = \sqrt{36 + 9}
\]
\[
AC = \sqrt{45}
\]
\[
AC = 3\sqrt{5}
\]
\[
AC \approx 6.71
\]

Thus, the length of side \( AC \) is approximately 6.71 units.

Would you like more details or have any other questions?

### Related Questions:
1. How do you calculate the length of side \( AB \) using the distance formula?
2. What are the properties of a triangle given its coordinates?
3. Can the triangle \( ABC \) be classified based on its side lengths?
4. How do you determine if a triangle is right-angled using its vertices?
5. How can we find the area of triangle \( ABC \) using its vertices?

**Tip:** Always make sure the coordinates are substituted correctly into the distance formula to avoid calculation errors.

Triangle ABC has coordinates A(-2, 0), B(-5, 3), C(4, 3). What is the length of side AC?

Learn how to calculate the length of side AC in triangle ABC using the distance formula. This example works with the coordinates A(-2, 0) and C(4, 3) and demonstrates step-by-step calculations. Suitable for students in Grades 6-9.

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