What is the distance between (2,5) and (7,6)

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a coordinate plane, you can use the distance formula:

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

For the points \((2, 5)\) and \((7, 6)\):

1. \(x_1 = 2\), \(y_1 = 5\)
2. \(x_2 = 7\), \(y_2 = 6\)

Substitute these values into the formula:

\[
d = \sqrt{{(7 - 2)^2 + (6 - 5)^2}} = \sqrt{{5^2 + 1^2}} = \sqrt{{25 + 1}} = \sqrt{26}
\]

So, the distance between the points \((2, 5)\) and \((7, 6)\) is \(\sqrt{26}\), which is approximately \(5.10\) units.

Would you like any further details or have any questions?

Here are some related questions to explore:
1. How would the distance formula change in three-dimensional space?
2. What is the midpoint between \((2, 5)\) and \((7, 6)\)?
3. How would you find the distance between a point and a line?
4. What is the slope of the line passing through \((2, 5)\) and \((7, 6)\)?
5. How can the distance formula be derived from the Pythagorean theorem?

**Tip:** The distance formula is a direct application of the Pythagorean theorem to the coordinate plane!

Learn how to calculate the distance between the points (2, 5) and (7, 6) using the distance formula. This problem involves applying the Pythagorean theorem in a coordinate plane. Suitable for students in Grades 6-8.

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