To find the distance between two points \( A(1,1) \) and \( B(-2,7) \) in a coordinate plane, we use the distance formula:

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

Here, \((x_1, y_1)\) are the coordinates of point A and \((x_2, y_2)\) are the coordinates of point B. Substituting the given values:

\[ (x_1, y_1) = (1, 1) \]
\[ (x_2, y_2) = (-2, 7) \]

Now, plug these into the distance formula:

\[ \text{Distance} = \sqrt{((-2) - 1)^2 + (7 - 1)^2} \]
\[ \text{Distance} = \sqrt{(-3)^2 + 6^2} \]
\[ \text{Distance} = \sqrt{9 + 36} \]
\[ \text{Distance} = \sqrt{45} \]
\[ \text{Distance} = 3\sqrt{5} \]

So, the distance between points A and B is \( 3\sqrt{5} \).

Do you want any further details or have any questions?

Here are some related questions you might find interesting:
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**Tip:** Always double-check your calculations to avoid simple arithmetic errors, especially when working with square roots and distances.

Learn how to calculate the distance between two points A(1,1) and B(-2,7) using the distance formula in coordinate geometry. This problem involves applying the distance formula to find the precise distance between given points. Suitable for students in Grades 7-9.

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