Exploring Transformations: Calculate Image Coordinates in Geometry

A triangle has vertices at A(2, 3), B(4, 5), and C(3, 1). If the triangle is translated 3 units to the right and 2 units up, what are the coordinates of the new vertices A', B', and C'?

• A'(4, 5), B'(6, 7), C'(5, 3)

• A'(2, 3), B'(4, 5), C'(3, 1)

• A'(5, 3), B'(7, 5), C'(6, 1)

• A'(5, 5), B'(7, 7), C'(6, 3)

A rectangle with corners at (1, 1), (1, 4), (5, 1), and (5, 4) is reflected over the y-axis. What are the coordinates of the new corners after the reflection?

• (-1, 1), (-1, 4), (5, 1), (5, 4)

• (1, 1), (1, 4), (5, 1), (5, 4)

• (-1, -1), (-1, -4), (-5, -1), (-5, -4)

• [(-1, 1), (-1, 4), (-5, 1), (-5, 4)]

A square with vertices at (0, 0), (0, 2), (2, 0), and (2, 2) is rotated 90 degrees clockwise around the origin. What are the coordinates of the new vertices?

• [(0, 0), (2, 0), (0, -2), (2, -2)]

• (0, 0), (0, -2), (-2, 0), (-2, -2)

• (0, 0), (2, 2), (0, 2), (2, 0)

• (0, 0), (-2, 0), (0, 2), (-2, 2)

A point P(3, 4) is dilated from the origin by a scale factor of 2. What are the coordinates of the image point P'?

• (4, 6)

• (0, 0)

• (6, 8)

• (3, 8)

A pentagon has vertices at (1, 1), (2, 3), (3, 1), (4, 3), and (2, 0). If the pentagon is translated left by 2 units and down by 1 unit, what are the new coordinates of the vertices?

• [[-1,1],[0,3],[1,1],[2,3],[0,0]]

• [[1,0],[2,2],[3,0],[4,2],[2,1]]

• [[-1,0],[0,2],[1,0],[2,2],[0,-1]]

• [[0,1],[1,2],[2,1],[3,2],[1,-1]]

A circle with center at (2, 2) and radius 3 is translated 4 units to the left. What are the new coordinates of the center of the circle?

• (-1, 2)

• (0, 2)

• (2, 5)

• (-2, 2)

A triangle with vertices at (1, 2), (3, 4), and (5, 2) is reflected over the line y = x. What are the coordinates of the reflected triangle?

• (1, 2), (3, 4), (5, 2)

• The coordinates of the reflected triangle are (2, 1), (4, 3), and (2, 5).

• (4, 5), (2, 3), (5, 1)

• (2, 1), (3, 5), (4, 2)

A rectangle has vertices at (0, 0), (0, 3), (4, 0), and (4, 3). If it is rotated 180 degrees around the point (2, 1.5), what are the coordinates of the new vertices?

• (4, 0), (0, 0), (4, 3), (0, 3)

• [(4, 3), (4, 0), (0, 3), (0, 0)]

• (2, 1.5), (2, 3.5), (6, 1.5), (6, 3.5)

• (0, 0), (0, 3), (4, 3), (4, 0)

A point Q(-1, -2) is reflected over the line y = -x. What are the coordinates of the image point Q'?

• (-1, 2)

• (2, 1)

• (-2, -1)

• (1, 2)

A hexagon has vertices at (1, 1), (2, 3), (3, 1), (4, 3), (5, 1), and (3, 0). If the hexagon is dilated from the origin by a scale factor of 0.5, what are the coordinates of the new vertices?

• [(0.5, 0.5), (1, 1), (1.5, 0.5), (2, 1), (2.5, 0.5), (1.5, 0)]

• [(0.5, 0.5), (1, 1), (1.5, 0.5), (2, 1.5), (2.5, 1), (1.5, 0.5)]

• [(0.5, 0.5), (1, 1.5), (1.5, 0.5), (2, 1.5), (2.5, 0.5), (1.5, 0)]

• [(1, 1), (2, 3), (3, 1), (4, 3), (5, 1), (3, 0)]