In parallelogram ABCD, slope of AB = -2, slope of BC = `3/(5)`. State the slope of
the altitude to CD

Answer

To find the slope of the altitude to side CD in parallelogram ABCD, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the slopes of the sides of the parallelogram:**
- Given: Slope of AB = -2
- Given: Slope of BC = 3/5

2. **Use the properties of parallelograms:**
- In a parallelogram, opposite sides are parallel, which means:
- Slope of AB = Slope of CD
- Slope of BC = Slope of AD
- Therefore, we have:
- Slope of CD = -2
- Slope of AD = 3/5

3. **Determine the slope of the altitude to CD:**
- The altitude to line CD is a line that is perpendicular to CD.
- The relationship between the slopes of two perpendicular lines is given by:
\[ \text{slope of line 1} \times \text{slope of line 2} = -1 \]
- Let the slope of the altitude (line CE) be denoted as \( m_{CE} \).
- Thus, we can write:
\[ \text{slope of CD} \times m_{CE} = -1 \]
- Substituting the slope of CD:
\[ -2 \times m_{CE} = -1 \]

4. **Solve for the slope of the altitude (m_{CE}):**
- Rearranging the equation:
\[ m_{CE} = \frac{-1}{-2} = \frac{1}{2} \]

5. **Conclusion:**
- The slope of the altitude to side CD is \( \frac{1}{2} \).