Exploring Geometry: Identifying Transformations in Shapes

A triangle is translated 5 units to the right and 3 units up. If the original vertex of the triangle is at (2, 3), where is the new vertex located?

• (5, 6)

• (2, 0)

• (7, 3)

• (7, 6)

A rectangle has vertices at (1, 1), (1, 4), (3, 1), and (3, 4). If the rectangle is reflected over the y-axis, what are the coordinates of the new vertices?

• (-1, 1), (-1, 4), (3, 1), (3, 4)

• [(-1, 1), (-1, 4), (-3, 1), (-3, 4)]

• (1, 1), (1, 4), (3, 1), (3, 4)

• (2, 1), (2, 4), (4, 1), (4, 4)

A square is rotated 90 degrees clockwise around its center. If one vertex of the square is at (2, 2), what are the coordinates of that vertex after the rotation?

• (2, 2)

• (2, -2)

• (4, 2)

• (0, 2)

A pentagon is translated left by 4 units and down by 2 units. If one vertex of the pentagon is at (6, 5), where will that vertex be after the translation?

• (2, 5)

• (2, 3)

• (6, 3)

• (10, 5)

A triangle is reflected over the line y = x. If the original triangle has vertices at (2, 3), (4, 5), and (6, 7), what are the coordinates of the reflected triangle?

• (2, 4), (4, 6), (6, 8)

• (3, 4), (5, 6), (7, 8)

• (1, 2), (3, 4), (5, 6)

• The coordinates of the reflected triangle are (3, 2), (5, 4), and (7, 6).

A rectangle is dilated by a scale factor of 2. If the original rectangle has a length of 3 units and a width of 2 units, what will be the new dimensions of the rectangle?

• Length: 6 units, Width: 4 units

• Length: 6 units, Width: 3 units

• Length: 4 units, Width: 2 units

• Length: 5 units, Width: 3 units

A shape is rotated 180 degrees around the origin. If a point on the shape is at (-3, 4), what are the coordinates of the point after the rotation?

• (3, -4)

• (-3, -4)

• (3, 4)

• (-4, 3)

A trapezoid is translated 6 units to the left. If one of its vertices is at (8, 2), what will be the new coordinates of that vertex?

• (8, 2)

• (2, 2)

• (14, 2)

• (2, 8)

A circle is translated 3 units down. If the center of the circle is at (5, 5), where is the new center located?

• (5, 2)

• (8, 5)

• (2, 5)

• (5, 8)

A hexagon is reflected over the x-axis. If one vertex of the hexagon is at (4, -3), what will be the coordinates of that vertex after the reflection?

• (4, -4)

• (4, 3)

• (-4, 3)

• (4, -3)