Question 1: A triangle is translated 4 units right and then reflected across the y-axis. Describe the single transformation that results in the same final position of the triangle.

Answer: Reflection across y-axis combined with translation right 4 units

Question 2: Construct a shape that is rotated 90° clockwise about the origin, then translated 3 units up. Draw the equivalent single transformation.

Answer: Rotation 90° clockwise + translation up 3 units

Question 3: A figure reflects over the x-axis and then translates 2 units left. What is the single transformation equivalent to these two?

Answer: Reflection over x-axis + translation left 2 units

Question 4: Plot the graph of y=2x on your grid and then perform a vertical shift up 3 units. Write the equation of the resulting graph as a single transformation.

Answer: y=2x+3 (vertical translation up 3 units)

Question 5: A shape is translated 5 units right, then reflected across the y-axis, and finally rotated 180° about the origin. Describe the equivalent single transformation.

Answer: Rotation 180° about origin + reflection over y-axis + translation right 5 units

Question 6: A rectangle is reflected over the line y = x and then translated 4 units down. Determine the single transformation that achieves the same result.

Answer: Reflection over y=x + translation down 4 units

Question 7: A triangle undergoes a rotation of 45° clockwise and then a translation 2 units left and 3 units up. Write the single transformation that combines these steps.

Answer: Rotation 45° clockwise + translation left 2 units + up 3 units

Question 8: Construct a figure that results from reflecting across the y-axis, then rotating 180° about the origin. Draw the equivalent single transformation.

Answer: Rotation 180° about origin + reflection over y-axis

Question 9: A shape is translated 3 units down and then reflected across the x-axis. What single transformation can be applied to achieve the same final shape?

Answer: Reflection over x-axis + translation down 3 units

Question 10: A figure is rotated 270° clockwise about the origin and then translated 5 units right. Write the combined single transformation.

Answer: Rotation 270° clockwise + translation right 5 units

Question 11: Error Analysis: A student states that rotating a figure 180° and then translating it 3 units left is the same as translating first and then rotating 180°. Is this correct? Explain and correct if necessary.

Answer: Incorrect; the order of transformations affects the outcome. To correct, specify the sequence as either rotation then translation or translation then rotation, both produce different results.