5. Find the distance between $$ P(2,8) $$ and $$ Q(5,3) $$ 9 34 $$ \sqrt{18} $$ $$ \sqrt{34} $$

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To find the distance between the points $$ P(2, 8) $$ and $$ Q(5, 3) $$, you can use the **distance formula**, which is derived from the Pythagorean theorem:

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

**Step-by-Step Calculation:**

1. **Identify the coordinates:**
   - $$ P(2, 8) $$ where $$ x_1 = 2 $$ and $$ y_1 = 8 $$
   - $$ Q(5, 3) $$ where $$ x_2 = 5 $$ and $$ y_2 = 3 $$

2. **Subtract the corresponding coordinates:**
   - Difference in $$ x $$-coordinates: $$ x_2 - x_1 = 5 - 2 = 3 $$
   - Difference in $$ y $$-coordinates: $$ y_2 - y_1 = 3 - 8 = -5 $$

3. **Square both differences:**
   - $$ (3)^2 = 9 $$
   - $$ (-5)^2 = 25 $$

4. **Add the squared differences:**
   - $$ 9 + 25 = 34 $$

5. **Take the square root of the sum:**
   - $$ \sqrt{34} $$

**Final Answer:**
$$
\sqrt{34}
$$

So, the distance between points $$ P(2, 8) $$ and $$ Q(5, 3) $$ is $$ \sqrt{34} $$.
The distance between $$ P(2,8) $$ and $$ Q(5,3) $$ is $$ \sqrt{34} $$.

5. Find the distance between \( P(2,8) \) and \( Q(5,3) \) 9 34 \( \sqrt{18} \) \( \sqrt{34} \)

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