Which of the following points is the nearest to the origin?

Options

A. (0,-6)
B. (-8,0)
C. (-3,-4)
D. (7,0)

Answer

To determine which of the given points is nearest to the origin (0, 0), we will use the distance formula. The distance \( d \) from a point \( (x, y) \) to the origin is given by the formula:

\[ d = \sqrt{x^2 + y^2} \]

We will calculate the distance for each of the given points and then compare them to find the minimum distance.

### Step 1: Identify the points
Let's assume the four points given are:
1. Point A: (0, -6)
2. Point B: (-8, 0)
3. Point C: (-3, -4)
4. Point D: (0, 7)

### Step 2: Calculate the distance for each point

**For Point A (0, -6):**
\[ d_A = \sqrt{0^2 + (-6)^2} = \sqrt{0 + 36} = \sqrt{36} = 6 \]

**For Point B (-8, 0):**
\[ d_B = \sqrt{(-8)^2 + 0^2} = \sqrt{64 + 0} = \sqrt{64} = 8 \]

**For Point C (-3, -4):**
\[ d_C = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

**For Point D (0, 7):**
\[ d_D = \sqrt{0^2 + 7^2} = \sqrt{0 + 49} = \sqrt{49} = 7 \]

### Step 3: Compare the distances
Now we have the distances:
- \( d_A = 6 \)
- \( d_B = 8 \)
- \( d_C = 5 \)
- \( d_D = 7 \)

The smallest distance is \( d_C = 5 \).

### Conclusion
Thus, the point nearest to the origin is Point C: **(-3, -4)**.

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