Question 1: Given a triangle with vertices at (2, 3), (4, 5), and (3, 7), construct its enlargement from the origin with a scale factor of 3. Draw the image on the grid.

Answer: See full answer key

Question 2: If a point A at (6, 2) is enlarged from the origin with a scale factor of 0.5, what are the coordinates of the image point A'?

Answer: 3, 1

Question 3: Construct a line segment from the origin to (4, 6). Enlarge it from the origin with a scale factor of 2. Show the enlarged segment.

Answer: See full answer key

Question 4: Enlarge a point at (1, 4) from the origin with a scale factor of 0.25. What are the new coordinates?

Answer: 0.25, 1

Question 1: A point P at (3, 4) is enlarged from the origin with a scale factor of 4. Another point Q is at (5, 1). If Q is also enlarged with the same scale factor from the origin, which point is further from the origin after enlargement?

Answer: Q is further from the origin after enlargement.

Question 2: A figure is enlarged from point A(2, 3) with a scale factor of 2. The original figure's vertex at (4, 5) is mapped to (8, 10). Identify the coordinates of point A and explain whether the enlargement is correctly performed.

Answer: A is at (1, 1.5); yes, the enlargement is correct.

Question 3: Construct an enlargement of a triangle with vertices at (1, 1), (2, 3), and (4, 2) from the origin with a scale factor of 3. Describe the steps.

Answer: Multiply each coordinate by 3 to get (3,3), (6,9), (12,6).

Question 4: A point at (x, y) is enlarged from the origin with scale factor k. Write the general formula for the image point.

Answer: Image point = (kx, ky)

Question 1: An architect designs a small model of a building that is enlarged by a scale factor of 10 from a reference point at the corner. If the model's side length measures 3 meters, what is the actual length of the building?

Answer: 30 meters

Question 2: A map shows a park with a distance of 5 cm between two points. The map is an enlargement from a point with a scale factor of 50. What is the actual distance in meters?

Answer: 2.5 meters

Question 3: A company is designing a new logo that will be enlarged from a starting shape using a scale factor of 4. If the original shape's coordinates are at (2, 2), what are the coordinates after enlargement?

Answer: 8, 8

Question 1: A figure is enlarged from point (1, 2) with a scale factor of 5. The original figure has a vertex at (3, 4). Find the new coordinates of this vertex and verify if the scale factor is applied correctly.

Answer: New coordinates: (13, 22); scale factor applied correctly.

Question 2: A student claims that enlarging from a point with a negative scale factor results in a smaller image. Is this true? Explain your reasoning.

Answer: False; a negative scale factor reflects the image across the point, not just shrinking it.

Question 1: A student enlarges a point at (2, 3) from the origin with a scale factor of 0.5 and gets (1, 1.5). Is this correct? If not, identify the mistake and provide the correct image point.

Answer: No, incorrect calculation; correct point is (1, 1.5). The student’s answer is correct, so the mistake does not exist here.

Question 2: A student attempts to enlarge a triangle from point (0,0) with scale factor 2, but they only multiply the x-coordinates by 2. What is the mistake, and how should it be corrected?

Answer: Mistake: they only multiplied x-coordinates. Both x and y coordinates should be multiplied by 2.

Question 3: A student claims that enlarging from a point always increases the size of the figure. Is this statement true? Explain why or why not.

Answer: False; if the scale factor is between 0 and 1, the figure shrinks, but it still enlarges if factor > 1.