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To find the distance between the two points \((1, 7)\) and \((-6, 4)\), we can use the **distance formula**:

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

Here, \((x_1, y_1)\) is \((1, 7)\) and \((x_2, y_2)\) is \((-6, 4)\).

### Step-by-Step Calculation:
1. Subtract the x-coordinates: \((-6) - (1) = -7\)
2. Subtract the y-coordinates: \(4 - 7 = -3\)
3. Square the differences: 
   \((-7)^2 = 49\) and \((-3)^2 = 9\)
4. Add the squares: \(49 + 9 = 58\)
5. Take the square root: 
   \[
   \sqrt{58} \approx 7.6
   \]

Therefore, the distance between the two points, rounded to the nearest tenth, is **7.6**.

Would you like more details on any part of this solution?

Here are some related questions to extend your understanding:
1. What is the general form of the distance formula?
2. How would the calculation change if the coordinates were negative?
3. Can you calculate the midpoint of these two points?
4. What is the significance of rounding to the nearest tenth in measurements?
5. How would the formula apply in a 3-dimensional space?

**Tip**: Always square the differences first before adding them, to avoid sign errors when working with negative coordinates!

Find the distance between the two points rounding to the nearest tenth: (1, 7) and (-6, 4).

Learn how to find the distance between the two points (1, 7) and (-6, 4) using the distance formula. The step-by-step solution includes applying the Pythagorean Theorem and rounding the result to the nearest tenth. Suitable for students in Grades 8-10.

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