Find the distance between $$ (3,4) $$ and $$ (4,-6) $$. If necessary, round to the nearest tenth. 2 units 10 units 7.3 units 53 units

Question

UpStudy AI · Accepted Answer

To find the distance between the points $$ (3, 4) $$ and $$ (4, -6) $$, 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:**
   - Point 1: $$ (x_1, y_1) = (3, 4) $$
   - Point 2: $$ (x_2, y_2) = (4, -6) $$

2. **Calculate the differences:**
   - $$ x_2 - x_1 = 4 - 3 = 1 $$
   - $$ y_2 - y_1 = -6 - 4 = -10 $$

3. **Plug the differences into the formula:**
   $$
   \text{Distance} = \sqrt{1^2 + (-10)^2} = \sqrt{1 + 100} = \sqrt{101}
   $$

4. **Compute the square root:**
   $$
   \sqrt{101} \approx 10.05 \text{ units}
   $$
   Rounding to the nearest tenth gives **10.0 units**.

**Conclusion:**

Among the provided options, **10 units** is the closest to the calculated distance.

**Answer:** 10 units
The distance between the points $$ (3,4) $$ and $$ (4,-6) $$ is approximately 10 units.

Find the distance between \( (3,4) \) and \( (4,-6) \). If necessary, round to the nearest tenth. 2 units 10 units 7.3 units 53 units