Which of the points A(-5, 0), B(0, -3), C(3, 0), D(0,4) are closer to the origin ?

Options

A. `A`
B. B
C. D
D. Points B and C both

Answer

To determine which of the points A(-5, 0), B(0, -3), C(3, 0), and D(0, 4) are closer to the origin (0, 0), we will calculate the distance of each point from the origin using the distance formula.

### Step-by-Step Solution:

1. **Identify the Distance Formula**:
The distance \( d \) between a point \( (x, y) \) and the origin \( (0, 0) \) is given by the formula:
\[ d = \sqrt{(x - 0)^2 + (y - 0)^2} = \sqrt{x^2 + y^2} \]

2. **Calculate the Distance for Point A(-5, 0)**:
\[ d_A = \sqrt{(-5)^2 + (0)^2} = \sqrt{25 + 0} = \sqrt{25} = 5 \]

3. **Calculate the Distance for Point B(0, -3)**:
\[ d_B = \sqrt{(0)^2 + (-3)^2} = \sqrt{0 + 9} = \sqrt{9} = 3 \]

4. **Calculate the Distance for Point C(3, 0)**:
\[ d_C = \sqrt{(3)^2 + (0)^2} = \sqrt{9 + 0} = \sqrt{9} = 3 \]

5. **Calculate the Distance for Point D(0, 4)**:
\[ d_D = \sqrt{(0)^2 + (4)^2} = \sqrt{0 + 16} = \sqrt{16} = 4 \]

6. **Compare the Distances**:
- Distance from origin to A: \( d_A = 5 \)
- Distance from origin to B: \( d_B = 3 \)
- Distance from origin to C: \( d_C = 3 \)
- Distance from origin to D: \( d_D = 4 \)

7. **Determine the Closest Points**:
The minimum distance is \( 3 \), which corresponds to points B and C.

### Conclusion:
The points that are closer to the origin are **B(0, -3)** and **C(3, 0)**.

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