Symmetry and transformations

A translation moves a shape without changing its orientation. A rotation turns it about a point. A reflection makes a mirror image on the other side of an axis. Compare the positions and orientations and look at the indicated axis or arrow.

Central symmetry about O is equivalent to a 180° rotation. The point O(5, 5) must be the midpoint of the segment joining the original point and its image.

1. Find the distance of the original x-coordinate from 5.
2. Move the same distance to the other side of the centre. The new x-coordinate is 10 − x.
3. Do the same for the y-coordinate. The new y-coordinate is 10 − y.

Answer form: A′(10 − x, 10 − y).

The first coordinate x gives the horizontal position and the second y gives the vertical position. Moving right adds the horizontal shift to x; moving up adds the vertical shift to y. Write the result as (new x; new y).

The first coordinate x gives the horizontal position and the second y gives the vertical position. Moving right adds the horizontal shift to x; moving up adds the vertical shift to y. Write the result as (new x; new y).

A line of symmetry divides a shape into two mirror-image halves. A scalene triangle has 0 lines, an isosceles triangle that is not equilateral has 1, a rectangle that is not a square has 2, an equilateral triangle has 3 and a square has 4. Choose the shape with the required count.

Reflecting a point across a vertical line does not change its height: the second coordinate stays the same. Only the first coordinate changes.

1. Find the horizontal distance from point A to the mirror line.
2. Place the reflected point the same distance on the other side of the line.
3. Read the new first coordinate and keep the original second coordinate.

Check that the mirror line lies exactly halfway between the original and reflected points.

A quarter turn is 90°, a half turn is 180° and three quarters is 270°. Clockwise directions follow this order: up → right → down → left → up. Count the required quarter turns.

Central symmetry about O is equivalent to a 180° rotation. The point O(5, 5) must be the midpoint of the segment joining the original point and its image.

1. Find the distance of the original x-coordinate from 5.
2. Move the same distance to the other side of the centre. The new x-coordinate is 10 − x.
3. Do the same for the y-coordinate. The new y-coordinate is 10 − y.

Answer form: A′(10 − x, 10 − y).

A quarter turn is 90°, a half turn is 180° and three quarters is 270°. Clockwise directions follow this order: up → right → down → left → up. Count the required quarter turns.