Determine the distance between $$ P(-3,-2) $$ and $$ B(-8 ; 2) $$, giving your answer as an exact value.

Question

UpStudy AI · Accepted Answer

To determine the distance between the points $$ P(-3, -2) $$ and $$ B(-8, 2) $$, we can use the **distance formula**:

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

**Step-by-Step Calculation:**

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

2. **Calculate the differences:**
   - $$ x_2 - x_1 = -8 - (-3) = -5 $$
   - $$ y_2 - y_1 = 2 - (-2) = 4 $$

3. **Plug the differences into the distance formula:**
   $$
   \text{Distance} = \sqrt{(-5)^2 + 4^2} = \sqrt{25 + 16} = \sqrt{41}
   $$

So, the exact distance between points $$ P $$ and $$ B $$ is:

$$
\boxed{\sqrt{41}}
$$
The distance between points $$ P(-3, -2) $$ and $$ B(-8, 2) $$ is $$ \sqrt{41} $$.

Determine the distance between \( P(-3,-2) \) and \( B(-8 ; 2) \), giving your answer as an exact value.