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To find the distance between the two points, (4, 6) and (7, 8), we can use the distance formula, which is derived from the Pythagorean theorem:

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

### Step 1: Identify the coordinates
- Point 1: \( (x_1, y_1) = (4, 6) \)
- Point 2: \( (x_2, y_2) = (7, 8) \)

### Step 2: Substitute into the distance formula
\[
\text{Distance} = \sqrt{(7 - 4)^2 + (8 - 6)^2}
\]

### Step 3: Calculate each part
1. \( 7 - 4 = 3 \) and \( 3^2 = 9 \)
2. \( 8 - 6 = 2 \) and \( 2^2 = 4 \)

### Step 4: Add and find the square root
\[
\text{Distance} = \sqrt{9 + 4} = \sqrt{13}
\]

### Step 5: Approximate the result
To the nearest tenth:
\[
\sqrt{13} \approx 3.6
\]

### Answer
The distance between the points (4, 6) and (7, 8) is approximately **3.6** units.

Would you like a detailed explanation of any steps, or do you have questions about this solution?

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Here are some additional related questions:
1. How is the Pythagorean theorem used in finding the distance between two points?
2. What is the significance of the distance formula in coordinate geometry?
3. How do you determine if a triangle is a right triangle on a coordinate plane?
4. What is the distance between points if both points lie on the same x- or y-coordinate?
5. How would the distance change if the points were (4, 6) and (10, 12)?

**Tip:** Remember that you can verify distances between points by visualizing or sketching a right triangle on a coordinate plane.

Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points, to the nearest tenth. Points: (4, 6) and (7, 8).

Learn how to calculate the distance between two points, (4,6) and (7,8), on a coordinate plane by forming a right triangle and applying the distance formula. This solution provides a step-by-step explanation and rounds the answer to the nearest tenth. Suitable for Grades 8-10.

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