Question

question 2 (39 points)
what are the coordinates for
a = ( , ) b = ( , ) c = ( , )
a = ( , ) b = ( , ) c = ( , )
each one is multiplied by what to get the scale factor of (you can use fraction or decimal)

Explanation:

Step1: Determine Coordinates

• For point A: Locate on grid, x = 2, y = 4.
• For point B: Locate on grid, x = 6, y = 2.
• For point C: Locate on grid, x = 1, y = 2.
• For point A': Locate on grid, x = 4, y = 10.
• For point B': Locate on grid, x = 14, y = 5.
• For point C': Locate on grid, x = 5, y = 5.

Step2: Calculate Scale Factor

• Take x - coordinate of A and A', \( \frac{4}{2}=2 \), \( \frac{10}{4} = 2.5 \).
• Take x - coordinate of B and B', \( \frac{14}{6}\approx2.33 \) (incorrect), \( \frac{5}{2}=2.5 \).
• Confirm with C and C', \( \frac{5}{1}=5 \) (incorrect for x - coordinate, but y - coordinate \( \frac{5}{2}=2.5 \)).
• Since in dilation (assuming origin - centered), use ratio of y - coordinates (more consistent here). \( \frac{10}{4}=2.5 \), \( \frac{5}{2}=2.5 \), \( \frac{5}{2}=2.5 \).

Answer:

A = (2, 4), B = (6, 2), C = (1, 2), A' = (4, 10), B' = (14, 5), C' = (5, 5), Scale factor = 2.5