Question
Determine the distance between \( P(-3,-2) \) and \( B(-8 ; 2) \), giving your answer as an exact value.
Ask by Cross Li. in Singapore
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The distance between points \( P(-3, -2) \) and \( B(-8, 2) \) is \( \sqrt{41} \).
Solution
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:
\[
\boxed{\sqrt{41}}
\]
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Simplify this solution Bonus Knowledge
To determine the distance between the points \( P(-3, -2) \) and \( B(-8, 2) \), we can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting in the coordinates, where \( P(-3, -2) \) is \( (x_1, y_1) \) and \( B(-8, 2) \) is \( (x_2, y_2) \): \[ d = \sqrt{((-8) - (-3))^2 + (2 - (-2))^2} \] Calculating the differences: \[ d = \sqrt{((-8 + 3))^2 + (2 + 2)^2} \] \[ d = \sqrt{(-5)^2 + (4)^2} \] \[ d = \sqrt{25 + 16} \] \[ d = \sqrt{41} \] Thus, the distance between points \( P \) and \( B \) is \( \sqrt{41} \).
