Calculating Image Coordinates in Geometry Dilations

A triangle has vertices at A(2, 3), B(4, 5), and C(6, 1). If the triangle is dilated by a scale factor of 2 from the origin, what are the coordinates of the image triangle A'B'C'?

• A'(3, 5), B'(6, 8), C'(9, 4)

• A'(2, 3), B'(4, 5), C'(6, 1)

• A'(5, 7), B'(10, 12), C'(14, 3)

• A'(4, 6), B'(8, 10), C'(12, 2)

A rectangle has corners at (1, 1), (1, 4), (5, 1), and (5, 4). If the rectangle is dilated by a scale factor of 0.5 from the origin, what are the coordinates of the image rectangle?

• [(1, 1), (1, 4), (5, 1), (5, 4)]

• [(0, 0), (0, 2), (2, 0), (2, 2)]

• [(2, 2), (2, 8), (10, 2), (10, 8)]

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

A square with vertices at (0, 0), (0, 2), (2, 0), and (2, 2) is dilated by a scale factor of 3. What are the coordinates of the new square?

• [(0, 0), (0, 6), (6, 0), (6, 6)]

• [(1, 1), (1, 5), (5, 1), (5, 5)]

• [(0, 0), (0, 4), (4, 0), (4, 4)]

• [(0, 0), (0, 3), (3, 0), (3, 3)]

A circle with a radius of 4 units is centered at (3, 2). If the circle is dilated by a scale factor of 1.5, what will be the new radius and the center coordinates?

• New radius: 8 units, Center coordinates: (3, 2)

• New radius: 6 units, Center coordinates: (0, 0)

• New radius: 6 units, Center coordinates: (3, 2)

• New radius: 4 units, Center coordinates: (3, 2)

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

• [(2, 1), (4, 3), (6, 1), (8, 3), (10, 1)]

• [(2, 2), (4, 6), (6, 2), (8, 6), (10, 2)]

• [(3, 3), (6, 6), (9, 3), (12, 6), (15, 3)]

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

A triangle with vertices at (2, 2), (4, 6), and (6, 2) is dilated by a scale factor of 0.75. What are the coordinates of the image triangle?

• [(1, 1), (3, 5), (5, 1)]

• [(1.5, 1.5), (3, 4.5), (4.5, 1.5)]

• [(2, 2), (4, 6), (6, 6)]

• [(2.5, 2.5), (4.5, 5), (6.5, 2.5)]

A rectangle with dimensions 4 units by 6 units has its bottom-left corner at (2, 2). If it is dilated by a scale factor of 2, what are the new dimensions and the coordinates of the bottom-left corner?

• New dimensions: 10 units by 14 units; Bottom-left corner: (2, 2)

• New dimensions: 8 units by 12 units; Bottom-left corner: (2, 2)

• New dimensions: 6 units by 8 units; Bottom-left corner: (4, 4)

• New dimensions: 8 units by 12 units; Bottom-left corner: (4, 2)

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

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

• [(0.5, 0), (1, 1), (1, 2), (0.5, 3), (0, 2), (0, 1)]

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

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

A triangle with vertices at (3, 4), (5, 8), and (7, 4) is dilated by a scale factor of 1.5. What are the coordinates of the image triangle?

• [(4.5, 5), (7.5, 9), (10.5, 5)]

• [(4, 6), (6, 10), (8, 6)]

• [(4.5, 6), (7.5, 12), (10.5, 6)]

• [(3, 4), (5, 8), (7, 8)]

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

• [(0, 0), (2, 0), (3, 2), (1, 2)]

• [(0, 0), (4, 0), (6, 4), (2, 4)]

• [(0, 0), (4, 0), (5, 4), (2, 4)]

• [(0, 0), (4, 0), (6, 2), (2, 2)]