Question 1: If a shape is translated 5 units to the right and then rotated 90° clockwise around the origin, what is the new position of the point originally at (2, 3)?

Answer: The point is at (3, -2).

Question 2: Construct a triangle on the grid with vertices at (0, 0), (4, 0), and (2, 3). Then, reflect the triangle over the y-axis and translate it 3 units up. Describe the new coordinates of each vertex.

Answer: Vertices after reflection: (0,0), (-4,0), (-2,3). After translation up 3 units: (0,3), (-4,3), (-2,6).

Question 3: A shape undergoes a translation 3 units left and then a reflection over the x-axis. If a point on the shape was originally at (5, 4), where is it after these transformations?

Answer: The point is at (2, -4).

Question 4: A figure is rotated 180° about the origin and then translated 2 units down. If a point is initially at (-3, 7), what are its coordinates after the transformations?

Answer: The point is at (3, -5).

Question 5: A shape is reflected over the y-axis, then rotated 90° counterclockwise around the origin. If a point starts at (6, -2), where does it end up?

Answer: The point ends at (2, 6).

Question 6: Identify and correct the mistake in this transformation sequence: a shape is rotated 90° clockwise, then translated 4 units right, but the resulting shape appears at the wrong position.

Answer: Common mistake: mixing up the order of transformations or incorrect rotation direction. Correct sequence: rotate 90° clockwise, then translate right 4 units.

Question 7: Calculate the coordinates of a point that starts at (1, 2), is translated 4 units left, then reflected over the x-axis.

Answer: The point is at (-3, -2).

Question 8: Plot the graph of y = 2x, then perform a translation of 3 units up and 2 units right. What is the new equation of the line?

Answer: The new line is y = 2(x - 2) + 3 = 2x - 4 + 3 = 2x - 1.

Question 9: A figure is rotated 270° clockwise about the origin and then translated 5 units down. If a point starts at (3, 4), where will it be after the transformations?

Answer: The point is at (4, -2).

Question 10: A shape undergoes two transformations: first, a reflection over the y-axis, then a rotation 180° about the origin. If a point begins at (-2, 5), where is it after these steps?

Answer: The point is at (2, -5).

Question 11: Explain the error in this sequence: a shape is translated 4 units right, then rotated 90° clockwise, but the final position looks incorrect. What should be checked?

Answer: Check the order of transformations and the rotation direction; applying translation before rotation affects the outcome.