Translation and reflection

For grown-ups: this lesson in words

Years 4 to 6 · Maths

Translation and reflection: I can slide a shape, flip it in a mirror line, and describe what happened.

1. Here is a squared grid, numbered 0 to 8 along the bottom and up the side.

   A triangle sits on the grid. Its corners are A, B and C.

   Watch it slide 4 squares to the right. It does not turn, and it does not flip.

   A slide like this is a translation. The shape is still the same size and shape. Only its place has changed.

   Picture: A squared grid numbered 0 to 8 along and up. A shape with 3 corners: A 1 square along and 1 square up; B 3 squares along and 1 square up; C 1 square along and 3 squares up. The shape moves 4 squares right, to A 5 squares along and 1 square up; B 7 squares along and 1 square up; C 5 squares along and 3 squares up. Its old place is dashed.

2. Here is the triangle again. Corner A is at (1, 1).

   This time it slides 3 squares right and 2 squares up.

   To describe a translation, follow one corner. A goes from (1, 1) to (4, 3): 3 right, then 2 up.

   We say the triangle has been translated 3 right and 2 up. Say right or left first, then up or down.

   Picture: A squared grid numbered 0 to 8 along and up. A shape with 3 corners: A (1, 1); B (3, 1); C (1, 3). The shape moves 3 squares right and 2 squares up, to A (4, 3); B (6, 3); C (4, 5). Its old place is dashed.

3. Your turn: Point P slides across to point Q. Describe the translation. How far does P move, and which way?

   Picture: A squared grid numbered 0 to 6 along and up. Point P is 1 square along and 3 squares up. Point Q is 5 squares along and 3 squares up.

   Choose one:

   • 4 squares right
   • 4 squares left
   • 5 squares right
   • 4 squares up

   Answer

   The answer: 4 squares right

   P is 1 along and Q is 5 along, both 3 up. 1, 2, 3, 4: P moves 4 squares right.

   Picture: A squared grid numbered 0 to 6 along and up. Point P is 1 square along and 3 squares up. Point Q is 5 squares along and 3 squares up. A walker starts at point P and goes right, right, right, right, ending 5 squares along and 3 squares up.

Words to know

translation:

A slide. The shape moves without turning or flipping.

reflection:

A flip over a mirror line. The new shape is a mirror image.

mirror line:

The line a shape is flipped over. Each corner ends up the same distance away, other side.

x-axis:

The axis that goes across the grid.

y-axis:

The axis that goes up the grid.