A.On a coordinate plane (graph paper), create triangle LMN where LN is a

Question

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 \( LM \).