Question 1: If a triangle is translated 4 units right and then rotated 90° clockwise about its new position, what are the coordinates of the triangle's vertex originally at (2, 3)?

Answer: (6, 3)

Question 2: A rectangle is reflected across the y-axis and then dilated by a scale factor of 2 from the origin. If one vertex was at (3, 4), where is this vertex after both transformations?

Answer: (-6, 8)

Question 3: What is the resulting coordinate of a point initially at (5, -2) after a rotation of 180° about the origin followed by a translation 3 units down?

Answer: (-5, 0)

Question 4: Construct a triangle on the grid that has undergone a translation 3 units left and then a reflection across the x-axis. Describe the original position of the triangle based on your construction.

Answer: The original triangle was translated 3 units right and reflected across the x-axis.

Question 5: A square is rotated 45° clockwise and then dilated by a scale factor of 1.5 from its center. If a corner was at (4, 4), where is this corner after both transformations?

Answer: (2.12, 4.12)

Question 6: A point moves from (1, 2) to (3, 2) after a translation, then to (3, 5) after a rotation of 90° counter-clockwise. What is its initial position?

Answer: (2, 0)

Question 7: A shape is reflected across y=2 and then translated 3 units up. If a point of the shape is at (4, 3), where does it end up?

Answer: (4, 5)

Question 8: A figure undergoes a dilation with scale factor 0.5 from the origin, then is reflected across the x-axis. A vertex was at (8, 10). Find its new position.

Answer: (-4, -5)

Question 9: Identify and correct the mistake: A student reflects a shape over the y-axis, then rotates it 180° clockwise, but reports the final position as the same as the initial position. Explain what went wrong.

Answer: The student mixed up the order of transformations; the correct order is rotation then reflection.

Question 10: A triangle is translated 5 units right and 3 units up, then rotated 90° clockwise. If one vertex was at (0, 0), where is it after both transformations?

Answer: (5, -3)

Question 11: A complex transformation involves translating a shape 2 units left, then dilating it by a factor of 2, then reflecting across the y-axis. Describe the sequence of transformations and their effect on a point at (3, 4).

Answer: Translate to (1, 4), dilate to (2, 8), reflect across y-axis to (-2, 8).