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

Answer

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

### Step 1: Understand the properties of a rectangle
In a rectangle, opposite sides are parallel, and adjacent sides are perpendicular to each other. This means that if we know the slope of one side, we can find the slope of the adjacent side using the relationship between their slopes.

### Step 2: Identify the slopes
Let:
- The slope of line segment AB be denoted as \( m_{AB} \).
- The slope of line segment BC be denoted as \( m_{BC} \).

From the problem, we know:
\[ m_{AB} = \frac{5}{6} \]

### Step 3: Use the property of perpendicular lines
For two lines that are perpendicular, the product of their slopes is equal to -1. Therefore, we can write:
\[ m_{AB} \cdot m_{BC} = -1 \]

### Step 4: Substitute the known slope into the equation
Substituting the value of \( m_{AB} \):
\[ \frac{5}{6} \cdot m_{BC} = -1 \]

### Step 5: Solve for \( m_{BC} \)
To find \( m_{BC} \), we rearrange the equation:
\[ m_{BC} = \frac{-1}{m_{AB}} = \frac{-1}{\frac{5}{6}} \]

### Step 6: Simplify the expression
When dividing by a fraction, we multiply by its reciprocal:
\[ m_{BC} = -1 \cdot \frac{6}{5} = -\frac{6}{5} \]

### Final Answer
Thus, the slope of line segment BC is:
\[ m_{BC} = -\frac{6}{5} \]