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To find the distance between two points \( P_1 = (0, 0) \) and \( P_2 = (6, 1) \), you can use the distance formula:

\[
d(P_1, P_2) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substitute the coordinates of \( P_1 \) and \( P_2 \):

\[
d(P_1, P_2) = \sqrt{(6 - 0)^2 + (1 - 0)^2}
\]
\[
d(P_1, P_2) = \sqrt{6^2 + 1^2}
\]
\[
d(P_1, P_2) = \sqrt{36 + 1}
\]
\[
d(P_1, P_2) = \sqrt{37}
\]

So, the exact distance is \( \sqrt{37} \).

Would you like further details or have any other questions?

Here are 5 related questions you might consider:
1. What is the distance between points \( P_1 = (2, 3) \) and \( P_2 = (5, 7) \)?
2. How do you find the midpoint between two points on a coordinate plane?
3. Can you find the distance formula in 3D for points \( P_1(x_1, y_1, z_1) \) and \( P_2(x_2, y_2, z_2) \)?
4. How is the distance formula derived from the Pythagorean theorem?
5. How can the distance formula be used in real-world applications?

**Tip**: When working with radicals, always simplify your result as much as possible for an exact answer.

Find the distance between the given points P1 = (0,0) and P2 = (6,1).

Learn how to find the distance between two points, P1 = (0,0) and P2 = (6,1), using the distance formula. This example uses key concepts from geometry and coordinate geometry and applies the Pythagorean theorem for solving. Suitable for students in Grades 8-10.

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