Question 1: Calculate the image of the point (3, 4) when enlarged from the origin with a scale factor of 2.

Answer: 6, 8

Question 2: If a point (x, y) is enlarged from the origin with scale factor 3, write the formula to find its new coordinates.

Answer: New point = (3x, 3y)

Question 3: A triangle has vertices at (1, 2), (4, 3), and (2, 5). If enlarged from the origin with a scale factor of 0.5, what are the new coordinates?

Answer: 0.5, 1; 2, 1.5; 1, 2.5

Question 4: Identify the mistake in the following reasoning: enlarging a point (x, y) from a different point (not the origin) with scale factor 4 results in coordinates (4x, 4y).

Answer: Misconception: Enlargement from a point other than the origin requires adjusting coordinates relative to that point, not simply multiplying by 4.

Question 5: Construct an enlargement of the point (-2, 3) from the origin with a scale factor of 1.5. Show the new coordinates.

Answer: -3, 4.5

Question 6: A shape scaled from the origin with a scale factor of 2 is incorrectly plotted with a scale factor of 3. Describe the error and how to correct it.

Answer: Incorrect scaling: the shape's points are 1.5 times larger, not 2. Correct by multiplying each point's coordinate by 2.

Question 7: Plot the graph of y = 2x for x values from -3 to 3.

Answer: Student draws the line y=2x on grid.

Question 8: Construct a triangle with vertices at (1, 1), (3, 1), and (2, 4). Enlarge it from the origin with a scale factor of 2 and show the new vertices.

Answer: 2, 2; 6, 2; 4, 8

Question 9: A student mistakenly applies a scale factor of 1.5 to a point (x, y) but forgets to multiply both coordinates. Explain the effect of this mistake.

Answer: Incorrectly enlarges only one coordinate, leading to incorrect image; both coordinates must be multiplied by the scale factor.

Question 10: Given a point (5, -2), enlarge it with a scale factor of 0.5 from the origin. What are the new coordinates?

Answer: 2.5, -1