Calculate the distance between the points $$ (3, 4) $$ and $$ (7, 1) $$.

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To calculate the distance between two points in a Cartesian plane, you can use the **Distance Formula**, which is derived from the Pythagorean theorem.

Given two points $$ P_1(x_1, y_1) $$ and $$ P_2(x_2, y_2) $$, the distance $$ d $$ between them is:

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

Let's apply this formula to your specific points $$ (3, 4) $$ and $$ (7, 1) $$.

1. **Identify the coordinates:**
   - $$ P_1 = (3, 4) $$ where $$ x_1 = 3 $$ and $$ y_1 = 4 $$
   - $$ P_2 = (7, 1) $$ where $$ x_2 = 7 $$ and $$ y_2 = 1 $$

2. **Subtract the corresponding coordinates:**
   - $$ x_2 - x_1 = 7 - 3 = 4 $$
   - $$ y_2 - y_1 = 1 - 4 = -3 $$

3. **Square these differences:**
   - $$ (x_2 - x_1)^2 = 4^2 = 16 $$
   - $$ (y_2 - y_1)^2 = (-3)^2 = 9 $$

4. **Add the squared differences:**
   - $$ 16 + 9 = 25 $$

5. **Take the square root of the sum to find the distance:**
   - $$ d = \sqrt{25} = 5 $$

**Therefore, the distance between the points $$ (3, 4) $$ and $$ (7, 1) $$ is 5 units.**
The distance between the points $$ (3, 4) $$ and $$ (7, 1) $$ is 5 units.

Calculate the distance between the points and .

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