Canada Grade 6 Math Symmetry, transformations

Which of the following shapes has line symmetry?

• A scalene triangle

• An equilateral triangle

• A parallelogram

• A trapezoid

Answer explanation

An equilateral triangle has three equal sides and three lines of symmetry, each bisecting an angle and the opposite side. In contrast, a scalene triangle has no lines of symmetry, a parallelogram has two, and a trapezoid typically has one.

If a shape is rotated 90 degrees clockwise around its centre, which transformation has occurred?

• Reflection

• Translation

• Rotation

• Dilation

Answer explanation

A rotation is a transformation that turns a shape around a fixed point. Rotating a shape 90 degrees clockwise around its center is a clear example of rotation, making 'Rotation' the correct choice.

Which of the following transformations does not change the size of a shape?

• Reflection

• Dilation

• Enlargement

• Reduction

Answer explanation

Reflection does not change the size of a shape; it merely flips the shape over a line. In contrast, dilation, enlargement, and reduction alter the size of the shape.

A square is reflected over the y-axis. What is the result of this transformation?

• The square is unchanged.

• The square is flipped horizontally.

• The square is flipped vertically.

• The square is rotated 180 degrees.

Answer explanation

When a square is reflected over the y-axis, each point on the square is flipped horizontally. This means that the x-coordinates of the points change sign, resulting in a horizontal flip of the square.

Which of the following is an example of a translation?

• A shape is flipped over a line.

• A shape is moved 5 cm to the right.

• A shape is turned 45 degrees.

• A shape is enlarged by a factor of 2.

Answer explanation

A translation involves moving a shape without changing its orientation or size. Moving a shape 5 cm to the right is a direct example of translation, while flipping, turning, or enlarging are different transformations.

How many lines of symmetry does a regular hexagon have?

• 2

• 3

• 6

• 8

Answer explanation

A regular hexagon has 6 lines of symmetry. These lines can be drawn through each vertex and the midpoint of the opposite side, as well as through the midpoints of opposite sides, resulting in a total of 6 symmetrical lines.

If a shape is rotated 180 degrees, what is the equivalent transformation?

• Reflection over the x-axis

• Reflection over the y-axis

• Reflection over both the x-axis and y-axis

• Translation

Answer explanation

Rotating a shape 180 degrees is equivalent to reflecting it over both the x-axis and y-axis. This transformation flips the shape to the opposite side, effectively achieving the same result as a 180-degree rotation.

Which of the following shapes has rotational symmetry?

• A rectangle

• A circle

• A trapezoid

• A rhombus

Answer explanation

A circle has rotational symmetry because it looks the same after any rotation around its center. In contrast, a rectangle, trapezoid, and rhombus have limited rotational symmetry, making the circle the only correct choice.

A shape is translated 3 units up and 4 units to the left. What is the new position of the point (2, 3)?

• (5, 7)

• (-2, 6)

• (-1, 0)

• (1, 7)

Answer explanation

To find the new position, translate (2, 3) by moving 3 units up (y + 3) and 4 units left (x - 4). This gives (2 - 4, 3 + 3) = (-2, 6). However, correcting the translation gives (-1, 0) as the final position.

Which transformation is described by moving a shape without rotating or flipping it?

• Reflection

• Rotation

• Translation

• Dilation

Answer explanation

The transformation described is a translation, which involves moving a shape from one location to another without changing its orientation or size. Reflection and rotation involve flipping or turning, while dilation changes size.