Find the distance of point `(5, -7)` from the origin.

Answer

To find the distance of the point (5, -7) from the origin (0, 0), we can use the distance formula. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

In this case, we have:
- Point A (the given point) = (5, -7) which means \(x_1 = 5\) and \(y_1 = -7\)
- Point B (the origin) = (0, 0) which means \(x_2 = 0\) and \(y_2 = 0\)

Now, we can substitute these values into the distance formula:

1. Calculate \(x_2 - x_1\):
\[ x_2 - x_1 = 0 - 5 = -5 \]

2. Calculate \(y_2 - y_1\):
\[ y_2 - y_1 = 0 - (-7) = 0 + 7 = 7 \]

3. Now, substitute these differences into the distance formula:
\[ d = \sqrt{(-5)^2 + (7)^2} \]

4. Calculate \((-5)^2\) and \(7^2\):
\[ (-5)^2 = 25 \quad \text{and} \quad 7^2 = 49 \]

5. Add these two results:
\[ 25 + 49 = 74 \]

6. Finally, take the square root:
\[ d = \sqrt{74} \]

Thus, the distance of the point (5, -7) from the origin is \(\sqrt{74}\).