Question 1: A triangle is enlarged with a scale factor of -2 from the origin. If one vertex is at (3, 4), what are the coordinates of the image after enlargement?

Answer: (-6, -8)

Question 2: Construct a triangle with vertices at (1, 2), (3, 4), and (5, 6). Enlarge it with a scale factor of -1.5 from the origin. Draw the image on the grid.

Answer: Students draw the enlarged triangle accordingly.

Question 3: A point at (2, -3) is rotated 180° about the origin. What are the new coordinates?

Answer: (-2, 3)

Question 4: Plot the graph of y = -2x. Identify at least two points that satisfy this equation and draw the line.

Answer: Any two points like (1, -2), (-1, 2).

Question 5: A square with vertices at (2, 2), (4, 2), (4, 4), and (2, 4) is enlarged with scale factor -2 from the origin. What are the coordinates of the enlarged square's vertices?

Answer: (-4, -4), (-8, -4), (-8, -8), (-4, -8)

Question 6: A figure is enlarged with a scale factor of -3 from point P(1, -2). If a vertex is initially at (4, 0), what are the coordinates of its image?

Answer: (-8, 4)

Question 7: A triangle is rotated 180° about the origin. The original vertices are (1, 3), (4, 0), and (2, -2). Find the new coordinates after rotation.

Answer: (-1, -3), (-4, 0), (-2, 2)

Question 8: Identify the common mistake made when students incorrectly assume the rotation angle during a transformation. Explain and correct it.

Answer: Students may confuse rotation and reflection. The correction involves clarifying that a 180° rotation about the origin results in points (x, y) becoming (-x, -y).

Question 9: A figure enlarged with scale factor -2 is rotated 180° about the origin. Describe the combined effect on the original figure in terms of transformation.

Answer: The figure undergoes a negative dilation (reflection and enlargement) combined with a 180° rotation, resulting in an image flipped and scaled, effectively a rotation combined with negative scaling effect.

Question 10: Using the grid, plot and enlarge a triangle with vertices at (0, 1), (2, 3), and (1, 4) with scale factor -1.5 about the origin. Describe the steps.

Answer: Students should multiply each coordinate by -1.5: (0,1)→(0,-1.5), (2,3)→(-3, -4.5), (1,4)→(-1.5, -6).

Question 11: Challenge: Prove that rotating a point (x, y) by 180° about the origin is equivalent to reflecting it across both axes. Show your working.

Answer: Rotation by 180° maps (x, y) to (-x, -y). Reflecting across the x-axis gives (x, -y); across y-axis gives (-x, y). Combining these reflections results in (-x, -y), confirming the rotation.