Find distance between the given pair of points. (5.2) and $$ (-7 .-3) $$

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To find the distance between the two points $$ A(5, 2) $$ and $$ B(-7, -3) $$, you can use the **Distance Formula**, which is derived from the Pythagorean theorem. The formula is:

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

**Step-by-Step Calculation:**

1. **Identify the coordinates:**
   - Point $$ A $$ has coordinates $$ (x_1, y_1) = (5, 2) $$
   - Point $$ B $$ has coordinates $$ (x_2, y_2) = (-7, -3) $$

2. **Subtract the corresponding coordinates:**
   - $$ x_2 - x_1 = -7 - 5 = -12 $$
   - $$ y_2 - y_1 = -3 - 2 = -5 $$

3. **Square both differences:**
   - $$ (-12)^2 = 144 $$
   - $$ (-5)^2 = 25 $$

4. **Add the squared differences:**
   - $$ 144 + 25 = 169 $$

5. **Take the square root of the sum:**
   - $$ \sqrt{169} = 13 $$

**Conclusion:**

The distance between points $$ A(5, 2) $$ and $$ B(-7, -3) $$ is **13 units**.
The distance between the points $$ (5, 2) $$ and $$ (-7, -3) $$ is 13 units.

Find distance between the given pair of points. (5.2) and \( (-7 .-3) \)

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