Mathematics
Coordinates and transformations
Class 7
Intermediate
About 20 min
Premium
Transformations on a grid: copying a rangoli motif
Flip, turn and slide a rangoli motif on a coordinate grid and watch where every corner lands.
Core concept
Reflections, rotations and translations move every point by a rule on its coordinates and keep the shape congruent
Topic: Coordinates and transformations
For Tihar, a rangoli is drawn on a courtyard marked out as a coordinate grid, with the origin O in the middle. A small motif with corners A(1, 1), B(4, 1) and C(1, 3) is copied around the courtyard to make the pattern. Each copy is made by a transformation: a reflection flips it in a mirror line, a rotation turns it about O, and a translation slides it along a vector. Every corner follows the same rule, so the copy keeps its size and shape.
What you will learn
- Find the image of a point after a reflection in the x-axis or the y-axis.
- Find the image of a point after a rotation of 90°, 180° or 270° about the origin.
- Translate a shape by a vector and describe the transformation in words and coordinates.
Before you start
- Read and plot points with negative coordinates.
Materials
- Squared paper, tracing paper and coloured powder or chalk
Equipment
- A ruler
Procedure
- Tap the flip chip to reflect the copy in the x-axis or the y-axis.
- Tap the turn chip to rotate the copy about O, anticlockwise.
- Tap the arrows to slide the copy one square at a time.
- Record a reflection in the y-axis, a quarter turn, a half turn, and a slide by the vector (−5, −4).
How this simulation is simplified
- Rotations are about the origin O, anticlockwise.