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To find the distance from the origin \((0,0)\) to the point \((3, -4)\), we use the distance formula:

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

Here:
- \(x_1 = 0\), \(y_1 = 0\) (the origin)
- \(x_2 = 3\), \(y_2 = -4\)

Substitute these values into the formula:

\[
d = \sqrt{(3 - 0)^2 + (-4 - 0)^2}
\]
\[
d = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]

Thus, the distance from the origin to the point \((3, -4)\) is **5 units**.

Would you like further details or have any questions?

Here are some related questions you might find helpful:
1. How is the distance formula derived from the Pythagorean theorem?
2. What is the distance between two general points, such as \((x_1, y_1)\) and \((x_2, y_2)\)?
3. How does the distance formula change in three dimensions?
4. Can the distance between two points ever be negative?
5. What are some real-life applications of the distance formula?

**Tip:** Always double-check your squared terms to avoid small calculation errors.

Find the distance from the origin out to the point (3, -4).

Learn how to calculate the distance from the origin to the point (3, -4) with the distance formula: d = √((x2 - x1)² + (y2 - y1)²). This step-by-step solution shows how the Pythagorean theorem is applied to find the distance in a coordinate plane. Suitable for Grades 6-8.

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