Question

#5-10: identify which line from the graph the following right triangles could lie on.
5.

6.

7.

8.

9.

10.

Explanation:

Step1: Find slope of each triangle

Slope = $\frac{\text{vertical side}}{\text{horizontal side}}$

• Triangle 5: $\frac{90}{120} = \frac{3}{4}$
• Triangle 6: $\frac{30}{10} = 3$
• Triangle 7: $\frac{18}{24} = \frac{3}{4}$
• Triangle 8: $\frac{21}{14} = \frac{3}{2}$
• Triangle 9: $\frac{36}{24} = \frac{3}{2}$
• Triangle 10: $\frac{48}{16} = 3$

Step2: Find slope of each line

Use grid points to calculate slope ($\frac{\Delta y}{\Delta x}$):

• Line A: $\frac{6}{2} = 3$
• Line B: $\frac{6}{4} = \frac{3}{2}$
• Line C: $\frac{6}{8} = \frac{3}{4}$

Step3: Match slopes to lines

Pair equal slopes:

• Slope $\frac{3}{4}$ → Line C
• Slope $3$ → Line A
• Slope $\frac{3}{2}$ → Line B

Answer:

1. LINE C
2. LINE A
3. LINE C
4. LINE B
5. LINE B
6. LINE A