Certainly! Let's find the distance between the two points (-1, 8) and (7, 0).
### Step 1: Identify the coordinates
We have two points:
- Point 1: [tex]\((-1, 8)\)[/tex]
- Point 2: [tex]\((7, 0)\)[/tex]
### Step 2: Calculate the difference in the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates
First, we need to find the differences in the [tex]\(x\)[/tex]-coordinates and [tex]\(y\)[/tex]-coordinates between the two points.
- Difference in [tex]\(x\)[/tex]-coordinates:
[tex]\(x_2 - x_1 = 7 - (-1) = 7 + 1 = 8\)[/tex]
- Difference in [tex]\(y\)[/tex]-coordinates:
[tex]\(y_2 - y_1 = 0 - 8 = -8\)[/tex]
So, the differences in coordinates are:
- [tex]\(x\)[/tex]-difference: [tex]\(8\)[/tex]
- [tex]\(y\)[/tex]-difference: [tex]\(-8\)[/tex]
### Step 3: Apply the Euclidean distance formula
The Euclidean distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Plug in the differences we calculated:
[tex]\[
\text{Distance} = \sqrt{(8)^2 + (-8)^2}
\][/tex]
### Step 4: Calculate the squared differences
[tex]\[
(8)^2 = 64
\][/tex]
[tex]\[
(-8)^2 = 64
\][/tex]
### Step 5: Sum the squared differences and compute the square root
[tex]\[
\text{Distance} = \sqrt{64 + 64} = \sqrt{128}
\][/tex]
### Step 6: Simplify the square root
[tex]\[
\sqrt{128} \approx 11.313708498984761
\][/tex]
So, the distance between the points (-1, 8) and (7, 0) is approximately 11.3137 units when rounded to four decimal places.
