Reflection and rotation
Reflect a shape in a vertical line, a slanted line and the x-axis, complete a shape from its half, rotate shapes about different points and find the coordinates of an image.
- Germany: grade 6
- Iran: grade 5
- Ukraine: grade 9
- Russia: grade 9
Guide
A reflection of a shape in a line is like its picture in a mirror. Each point goes the same distance to the other side of the line, and the segment joining a point and its image is perpendicular to the line. The line can be vertical, horizontal or slanted.
If a shape has a line of symmetry, its other half is the reflection of the first half. So we can complete a shape from its half.
In a rotation the shape turns about a point, the centre of rotation. Every vertex moves on a circle round that point and its distance from the centre does not change. Anticlockwise is the opposite way to a clock's hands.
In a half turn (180°) about the origin both coordinates change sign: (3, 2) becomes (−3, −2). A reflection in the x-axis changes only the sign of y, and one in the y-axis only the sign of x.
For each vertex, count its distance to the line or the centre and go the same distance on the other side.