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To find the distance between points \( A(4, -2) \) and \( C(9, 10) \), we can use the distance formula:

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

Substituting the coordinates of points \( A(4, -2) \) and \( C(9, 10) \):

\[
d = \sqrt{(9 - 4)^2 + (10 - (-2))^2}
\]

\[
d = \sqrt{(5)^2 + (12)^2}
\]

\[
d = \sqrt{25 + 144}
\]

\[
d = \sqrt{169} = 13
\]

Thus, the distance between points A and C is **13**. The correct answer is option **d**.

Do you need further clarification or details?

Here are 5 related questions:
1. How would you calculate the distance if the points had three dimensions?
2. What is the distance between two points that have the same \( x \)-coordinates?
3. How can the distance formula be derived from the Pythagorean theorem?
4. What is the equation of the line passing through points \( A(4, -2) \) and \( C(9, 10) \)?
5. How can you calculate the midpoint between points \( A \) and \( C \)?

**Tip:** When solving distance problems, always verify that you're substituting the correct coordinates into the formula, as small errors can easily occur.

Below is a triangle (ABC). The distance between A(4, -2) and C(9, 10) is?

Learn how to find the distance between two points A(4, -2) and C(9, 10) on a coordinate plane using the distance formula. This solution is based on key geometry and algebra concepts, suitable for students in grades 7-10.

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