Find the distance between (7,0) and (1, - 8).

Answer

To find the distance between the points (7, 0) and (1, -8), we can use the distance formula. The distance formula is given by:

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

Where:
- \((x_1, y_1)\) are the coordinates of the first point,
- \((x_2, y_2)\) are the coordinates of the second point.

### Step 1: Identify the coordinates
Let:
- Point A = (7, 0) → \(x_1 = 7\), \(y_1 = 0\)
- Point B = (1, -8) → \(x_2 = 1\), \(y_2 = -8\)

### Step 2: Substitute the coordinates into the distance formula
Now, substitute the values into the distance formula:

\[ d = \sqrt{(1 - 7)^2 + (-8 - 0)^2} \]

### Step 3: Calculate the differences
Calculate the differences:
- \(x_2 - x_1 = 1 - 7 = -6\)
- \(y_2 - y_1 = -8 - 0 = -8\)

### Step 4: Square the differences
Now square the differences:
- \((-6)^2 = 36\)
- \((-8)^2 = 64\)

### Step 5: Add the squared differences
Add the squared differences:

\[ d = \sqrt{36 + 64} \]

### Step 6: Simplify the expression
Now simplify the expression:

\[ d = \sqrt{100} \]

### Step 7: Calculate the square root
Finally, calculate the square root:

\[ d = 10 \]

### Conclusion
The distance between the points (7, 0) and (1, -8) is **10 units**.

---