In rect. ABCD, slope of `AB=5/(6)`. State the slope of DA

Answer

To find the slope of line DA in rectangle ABCD, given that the slope of line AB is \( \frac{5}{6} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of a Rectangle**: In a rectangle, opposite sides are equal and parallel, and adjacent sides are perpendicular to each other.

2. **Identify the Given Information**: We know that the slope of line AB (denoted as \( M_1 \)) is given as:
\[ M_1 = \frac{5}{6} \]

3. **Use the Perpendicularity Condition**: Since line DA is perpendicular to line AB, we can use the property of slopes of perpendicular lines. If two lines are perpendicular, the product of their slopes is -1. This can be expressed as:
\[ M_1 \cdot M_2 = -1 \]
where \( M_2 \) is the slope of line DA.

4. **Substitute the Known Slope**: Substitute the value of \( M_1 \) into the equation:
\[ \frac{5}{6} \cdot M_2 = -1 \]

5. **Solve for \( M_2 \)**: To find \( M_2 \), we can rearrange the equation:
\[ M_2 = \frac{-1}{\frac{5}{6}} = -1 \cdot \frac{6}{5} = -\frac{6}{5} \]

6. **Conclusion**: Therefore, the slope of line DA is:
\[ M_2 = -\frac{6}{5} \]

### Final Answer:
The slope of line DA is \( -\frac{6}{5} \).

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