Question 1: A triangle has vertices at A(2, 3), B(4, 5), and C(3, 2). If the triangle is rotated 180° about the origin, what are the new coordinates of point A?

Answer: A'(-2, -3)

Question 2: Construct a rotation of 270° clockwise about the origin for the point (1, -2). Draw the image on the grid.

Answer: The point is at (2, 1)

Question 3: A square has vertices at (1,1), (1,3), (3,3), and (3,1). If it is rotated 90° counter-clockwise about the origin, what are the coordinates of the new vertices?

Answer: (-1,1), (-3,1), (-3,3), (-1,3)

Question 4: Explain how a negative scale factor combined with rotation affects the shape and position of a figure.

Answer: A negative scale factor causes a figure to be reflected and enlarged or reduced, depending on the magnitude, and rotation can change its orientation. Together, they produce a figure that is reflected across an axis and rotated, altering its position and direction.

Question 5: A point (5, -2) is rotated 180° about the origin. What is its new position?

Answer: (-5, 2)

Question 6: Construct a triangle with vertices at (2, 2), (4, 2), and (3, 4). Rotate this triangle 180° about the origin. Draw the image on the grid.

Answer: Vertices at (-2, -2), (-4, -2), and (-3, -4)

Question 7: A rectangle with vertices at (1, 1), (1, 4), (5, 4), and (5, 1) undergoes a rotation of 180° about the origin. What are the new vertices?

Answer: (-1, -1), (-1, -4), (-5, -4), (-5, -1)

Question 8: A real-world scenario: A drone at position (3, -4) is instructed to perform a 180° rotation about the origin. Where will it be after rotation?

Answer: It will move to (-3, 4).

Question 9: What is the effect of combining a negative scale factor with a 180° rotation on a figure's orientation and size?

Answer: The figure is reflected across the origin, rotated 180°, and scaled negatively, resulting in a figure flipped and rotated, with size affected depending on scale magnitude.

Question 10: A triangle has vertices at (2, 3), (4, 5), and (3, 2). It is rotated 180° about the origin. Which vertex becomes (-4, -5)?

Answer: Vertex B (4, 5)

Question 11: Identify and correct the mistake: A student claims that rotating a figure 180° about the origin always results in the figure being in the same position after rotation.

Answer: Correction: Rotating 180° about the origin reflects and rotates the figure, but it generally changes position unless the figure is symmetric about the origin.