Calculate the length of a diagonal from the origin to the point $$ (6, 8) $$.

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To calculate the length of the diagonal (also known as the distance) from the origin $$(0, 0)$$ to the point $$(6, 8)$$ in a Cartesian coordinate system, you can use the **distance formula**. The distance formula is derived from the Pythagorean theorem and is given by:

$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

**Step-by-Step Calculation:**

1. **Identify the coordinates:**
   - Origin: $$(x_1, y_1) = (0, 0)$$
   - Given point: $$(x_2, y_2) = (6, 8)$$

2. **Plug the values into the distance formula:**
   $$
   \text{Distance} = \sqrt{(6 - 0)^2 + (8 - 0)^2}
   $$

3. **Simplify the expressions inside the parentheses:**
   $$
   \text{Distance} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64}
   $$

4. **Add the squared terms:**
   $$
   \text{Distance} = \sqrt{100}
   $$

5. **Take the square root:**
   $$
   \text{Distance} = 10
   $$

**Final Answer:** The length of the diagonal from the origin to the point $$(6, 8)$$ is **10 units**.
The length of the diagonal from the origin to the point (6, 8) is 10 units.

Calculate the length of a diagonal from the origin to the point .

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