Question
draw △LMN where LM is a vertical line segment whose length is a multiple of 3 and MN is a horizontal line segment whose length is a multiple of 6 plot point q on LM such that LQ / Qm = 1 / 2. Similarly , plot point R on MN such that NR / RM = 1 / 2. Connect points Q and R to create QR. explain detailed to draw
Answers
GPT-4o mini
To draw triangle \( \triangle LMN \) with the specified properties, follow these detailed steps:
### Step 1: Draw the Vertical Segment \( LM \)
1. **Choose the Length of \( LM \)**:
- Since \( LM \) must be a vertical line segment that is a multiple of 3, let's choose a length of \( 6 \) (which is \( 3 \times 2 \)).
2. **Draw the Line Segment**:
- Start by placing point \( L \) at coordinates \( (0, 0) \).
- Since \( LM \) is vertical, point \( M \) will also be directly above \( L \) on the y-axis. Thus, point \( M \) will be at \( (0, 6) \).
- Draw a vertical line from \( L \) to \( M \).
### Step 2: Draw the Horizontal Segment \( MN \)
1. **Choose the Length of \( MN \)**:
- \( MN \) needs to be a horizontal line segment whose length is a multiple of 6, so we will choose a length of \( 12 \) (which is \( 6 \times 2 \)).
2. **Position Point \( N \)**:
- Point \( N \) will be horizontally aligned with point \( M \). Since \( M \) is at \( (0, 6) \), point \( N \) will be at \( (12, 6) \).
- Draw a horizontal line from \( M \) to \( N \).
### Step 3: Mark Points \( Q \) and \( R \)
1. **Locate Point \( Q \) on Segment \( LM \)**:
- According to the ratio \( \frac{LQ}{QM} = \frac{1}{2} \), it means that segment \( LQ \) is one part, and \( QM \) is two parts.
- The entire length \( LM = 6 \) is divided into 3 equal parts, making each part \( 2 \).
- Thus, \( LQ = 2 \) and \( QM = 4 \).
- Hence, point \( Q \) will be at \( (0, 2) \).
2. **Locate Point \( R \) on Segment \( MN \)**:
- According to the ratio \( \frac{NR}{RM} = \frac{1}{2} \), segment \( NR \) is one part, and \( RM \) is two parts.
- The total length \( NM = 12 \) can be divided into 3 equal sections, with each section being \( 4 \).
- Thus, \( NR = 4 \) and \( RM = 8 \).
- Therefore, point \( R \) will be at \( (8, 6) \).
### Step 4: Connect Points \( Q \) and \( R \)
1. **Draw Line Segment \( QR \)**:
- Now connect points \( Q(0, 2) \) and \( R(8, 6) \) by drawing a straight line between them.
### Final Configuration:
- **Points**:
- \( L(0, 0) \)
- \( M(0, 6) \)
- \( N(12, 6) \)
- \( Q(0, 2) \)
- \( R(8, 6) \)
- **Line Segments**:
- Draw \( LM \) vertically.
- Draw \( MN \) horizontally.
- Connect \( Q \) to \( R \) with a diagonal line.
Your drawing will consist of triangle \( \triangle LMN \) with the points \( Q \) and \( R \) marked accordingly, satisfying the given ratio conditions.
### Step 1: Draw the Vertical Segment \( LM \)
1. **Choose the Length of \( LM \)**:
- Since \( LM \) must be a vertical line segment that is a multiple of 3, let's choose a length of \( 6 \) (which is \( 3 \times 2 \)).
2. **Draw the Line Segment**:
- Start by placing point \( L \) at coordinates \( (0, 0) \).
- Since \( LM \) is vertical, point \( M \) will also be directly above \( L \) on the y-axis. Thus, point \( M \) will be at \( (0, 6) \).
- Draw a vertical line from \( L \) to \( M \).
### Step 2: Draw the Horizontal Segment \( MN \)
1. **Choose the Length of \( MN \)**:
- \( MN \) needs to be a horizontal line segment whose length is a multiple of 6, so we will choose a length of \( 12 \) (which is \( 6 \times 2 \)).
2. **Position Point \( N \)**:
- Point \( N \) will be horizontally aligned with point \( M \). Since \( M \) is at \( (0, 6) \), point \( N \) will be at \( (12, 6) \).
- Draw a horizontal line from \( M \) to \( N \).
### Step 3: Mark Points \( Q \) and \( R \)
1. **Locate Point \( Q \) on Segment \( LM \)**:
- According to the ratio \( \frac{LQ}{QM} = \frac{1}{2} \), it means that segment \( LQ \) is one part, and \( QM \) is two parts.
- The entire length \( LM = 6 \) is divided into 3 equal parts, making each part \( 2 \).
- Thus, \( LQ = 2 \) and \( QM = 4 \).
- Hence, point \( Q \) will be at \( (0, 2) \).
2. **Locate Point \( R \) on Segment \( MN \)**:
- According to the ratio \( \frac{NR}{RM} = \frac{1}{2} \), segment \( NR \) is one part, and \( RM \) is two parts.
- The total length \( NM = 12 \) can be divided into 3 equal sections, with each section being \( 4 \).
- Thus, \( NR = 4 \) and \( RM = 8 \).
- Therefore, point \( R \) will be at \( (8, 6) \).
### Step 4: Connect Points \( Q \) and \( R \)
1. **Draw Line Segment \( QR \)**:
- Now connect points \( Q(0, 2) \) and \( R(8, 6) \) by drawing a straight line between them.
### Final Configuration:
- **Points**:
- \( L(0, 0) \)
- \( M(0, 6) \)
- \( N(12, 6) \)
- \( Q(0, 2) \)
- \( R(8, 6) \)
- **Line Segments**:
- Draw \( LM \) vertically.
- Draw \( MN \) horizontally.
- Connect \( Q \) to \( R \) with a diagonal line.
Your drawing will consist of triangle \( \triangle LMN \) with the points \( Q \) and \( R \) marked accordingly, satisfying the given ratio conditions.