Question

A.On a coordinate plane (graph paper), create triangle LMN where LN is a
vertical line segment and MN is a horizontal line segment.

B. then create QR parallel to LM such that Q is on LN and point r is on MN

c. Lable points L, M, N, Q and r with their coordinates

d. use the slope formula to confirm QR is parell to LM

Answer 1

To create triangle LMN with the specified conditions on a coordinate plane, we'll go through each step systematically.

### A. Create Triangle LMN

1. **Plot Points**:
- Let \( L(1, 3) \)
- Let \( M(4, 3) \) (horizontally aligned with L)
- Let \( N(1, 0) \) (vertically aligned with L)

2. **Draw Triangle**:
- Draw the vertical line segment \( LN \) from \( L(1, 3) \) to \( N(1, 0) \).
- Draw the horizontal line segment \( MN \) from \( M(4, 3) \) to \( N(1, 3) \).
- Connect points L and M to complete the triangle.

### B. Create QR Parallel to LM

1. **Identify Point Q on LN**:
- Let \( Q(1, 2) \) on the line segment \( LN \).

2. **Identify Point R on MN**:
- Since QR is parallel to LM, point R must have the same y-coordinate as points L and M. Therefore, let \( R(4, 2) \) on the line segment \( MN \).

### C. Label Points with Coordinates

- \( L(1, 3) \)
- \( M(4, 3) \)
- \( N(1, 0) \)
- \( Q(1, 2) \)
- \( R(4, 2) \)

### D. Use Slope Formula to Confirm QR is Parallel to LM

**Slope Formula**:
\[ Slope (m) = \frac{y_2 - y_1}{x_2 - x_1} \]

1. **Calculate Slope of LM**:
- For points \( L(1, 3) \) and \( M(4, 3) \):
\[
m_{LM} = \frac{3 - 3}{4 - 1} = \frac{0}{3} = 0
\]

2. **Calculate Slope of QR**:
- For points \( Q(1, 2) \) and \( R(4, 2) \):
\[
m_{QR} = \frac{2 - 2}{4 - 1} = \frac{0}{3} = 0
\]

### Conclusion

Since the slopes of both \( LM \) and \( QR \) are equal (both are 0), this confirms that \( QR \) is parallel to \( LM \).