Find the distance between the pair of points. $$ R(0,8), \mathrm{S}(3,2) $$ The exact distance is $$ 3 \sqrt{5} $$. (Type an exact answer, using radicals as needed.) The approximate distance is (Round to the nearest tenth as needed.)

Question

UpStudy AI · Accepted Answer

To find the distance between the points $$ R(0, 8) $$ and $$ S(3, 2) $$, 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:**
   - Point $$ R $$: $$ (x_1, y_1) = (0, 8) $$
   - Point $$ S $$: $$ (x_2, y_2) = (3, 2) $$

2. **Calculate the differences:**
   - $$ \Delta x = x_2 - x_1 = 3 - 0 = 3 $$
   - $$ \Delta y = y_2 - y_1 = 2 - 8 = -6 $$

3. **Apply the distance formula:**
   $$
   \text{Distance} = \sqrt{(3)^2 + (-6)^2} = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5}
   $$

### Exact Distance:
$$
3\sqrt{5}
$$

### Approximate Distance:
To find the approximate value, calculate $$ 3\sqrt{5} $$:

$$
\sqrt{5} \approx 2.236
$$
$$
3\sqrt{5} \approx 3 \times 2.236 = 6.708
$$

Rounded to the nearest tenth:
$$
6.7
$$

### **Final Answer:**
- **Exact distance:** $$ 3\sqrt{5} $$
- **Approximate distance:** $$ 6.7 $$ units
The distance between points $$ R(0,8) $$ and $$ S(3,2) $$ is $$ 3\sqrt{5} $$ units exactly, which is approximately 6.7 units.

Find the distance between the pair of points. \( R(0,8), \mathrm{S}(3,2) \) The exact distance is \( 3 \sqrt{5} \). (Type an exact answer, using radicals as needed.) The approximate distance is (Round to the nearest tenth as needed.)

Solución de tutoría real

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Geometry Questions