What is the distance between the points and ? Give your answer in radical form.
units

Ask by Vargas Harris. in the United States

Jan 15,2025

Question

What is the distance between the points $$ (5,7) $$ and $$ (-1,11) $$ ? Give your answer in radical form. $$ d=\square $$ units

UpStudy AI · Accepted Answer

To find the distance between the points $$ (5, 7) $$ and $$ (-1, 11) $$, we can use the **distance formula**:

$$
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

**Step-by-Step Calculation:**

1. **Identify the coordinates:**
   - Point 1: $$ (x_1, y_1) = (5, 7) $$
   - Point 2: $$ (x_2, y_2) = (-1, 11) $$

2. **Calculate the differences:**
   $$
   x_2 - x_1 = -1 - 5 = -6
   $$
   $$
   y_2 - y_1 = 11 - 7 = 4
   $$

3. **Square the differences:**
   $$
   (-6)^2 = 36
   $$
   $$
   4^2 = 16
   $$

4. **Add the squared differences:**
   $$
   36 + 16 = 52
   $$

5. **Take the square root to find the distance:**
   $$
   d = \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13}
   $$

**Final Answer:**

$$
d = \boxed{2\sqrt{13}} \text{ units}
$$
The distance between the points $$ (5,7) $$ and $$ (-1,11) $$ is $$ 2\sqrt{13} $$ units.

What is the distance between the points and ? Give your answer in radical form.
units