if A(3, 6), B(2, 1), C(7, 2) and D(8, 7) are the vertices of a quadrilateral ABCD. Find the slopes of AB, BC, CD and DA.

To find the slopes of the sides of quadrilateral ABCD, we use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

### 1. Slope of AB (between points A(3, 6) and B(2, 1)):

\[
\text{slope of AB} = \frac{1 - 6}{2 - 3} = \frac{-5}{-1} = 5
\]

### 2. Slope of BC (between points B(2, 1) and C(7, 2)):

\[
\text{slope of BC} = \frac{2 - 1}{7 - 2} = \frac{1}{5}
\]

### 3. Slope of CD (between points C(7, 2) and D(8, 7)):

\[
\text{slope of CD} = \frac{7 - 2}{8 - 7} = \frac{5}{1} = 5
\]

### 4. Slope of DA (between points D(8, 7) and A(3, 6)):

\[
\text{slope of DA} = \frac{6 - 7}{3 - 8} = \frac{-1}{-5} = \frac{1}{5}
\]

### Summary of Slopes:
- **Slope of AB**: \(5\)
- **Slope of BC**: \(\frac{1}{5}\)
- **Slope of CD**: \(5\)
- **Slope of DA**: \(\frac{1}{5}\)

These slopes indicate the directions of the sides of the quadrilateral ABCD.

Would you like more details or have any questions about this solution?

Here are five related questions you might consider:
1. How do parallel lines relate to the slopes of line segments?
2. Can the quadrilateral ABCD be classified as a specific type based on these slopes?
3. How would you find the length of each side of quadrilateral ABCD?
4. What are the equations of the lines AB, BC, CD, and DA?
5. How do you calculate the area of quadrilateral ABCD?

**Tip:** For parallel lines, the slopes of the corresponding sides will be equal.

Learn how to find the slopes of sides AB, BC, CD, and DA of quadrilateral ABCD using the slope formula. This problem covers basic concepts in analytic geometry, including calculating slopes between points. Suitable for Grades 7-9 students.

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