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To solve the problem of finding the distance between the two points \((1, 4)\) and \((6, -8)\), we can use the distance formula:

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

Given:
- \((x_1, y_1) = (1, 4)\)
- \((x_2, y_2) = (6, -8)\)

Let's substitute the coordinates into the formula:

\[
d = \sqrt{(6 - 1)^2 + (-8 - 4)^2}
\]
\[
d = \sqrt{(5)^2 + (-12)^2}
\]
\[
d = \sqrt{25 + 144}
\]
\[
d = \sqrt{169}
\]
\[
d = 13
\]

The distance between the two points is **13 units**. Since the problem asks to round to the nearest tenth (if necessary), and 13 is a whole number, no rounding is needed.

Would you like any additional details or have further questions? Here are five follow-up questions you might explore:

1. How is the distance formula derived from the Pythagorean theorem?
2. How can we generalize this formula to find the distance in three-dimensional space?
3. What other real-world applications can this distance formula have?
4. How does the distance formula relate to vector mathematics?
5. What happens when both points lie on the same line parallel to one of the axes?

**Tip:** When using the distance formula, always ensure to square both the horizontal and vertical differences before adding them together.

Find the distance between the two points (1, 4) and (6, -8), rounding to the nearest tenth if necessary.

Learn how to find the distance between the points (1, 4) and (6, -8) using the distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²). This problem is perfect for geometry students in grades 8-10, reinforcing the connection between coordinate systems and the Pythagorean Theorem.

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