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Lesson · Grade 7 · Mathematics

Does the Order of Transformations Matter?

  • Grade 7
  • Mathematics
  • 1 min 13 s
  • British Columbia
  • BC7-MA-63

A triangle on a grid is reflected in a mirror line and translated 5 squares left, once with the reflection first and once with the translation first, with the squares counted at each step. The two final images land 10 squares apart, showing that changing the order of transformations can change the final image.

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In one sentence

The question this lesson answers

Does the order of transformations matter?

Here is a triangle on a grid, beside a mirror line.

Transcript

What the lesson says

Does the order of transformations matter?

Here is a triangle on a grid, beside a mirror line.

We will reflect it in the mirror line and translate it 5 squares left.

Let us try the two steps in both orders, and compare.

For order one, first reflect the triangle in the mirror line.

Then translate that image 5 squares to the left.

This is where order one ends up.

For order two, start again and translate the triangle 5 squares left first.

Then reflect that image in the mirror line.

Its top corner is 3 squares from the line, so it lands 3 squares on the other side.

This is where order two ends up.

Now put the two final images side by side.

Same triangle and same two steps, but the final images land in different places.

So yes, for these two steps, the order matters.

Remember, changing the order of transformations can change the final image.

Curriculum

Where this fits

British Columbia, Grade 7

Mathematics, Geometry and measurement: combinations of transformationsBC7-MA-63

Previous: Combining Two Transformations

The outcomes and strands follow the British Columbia curriculum.

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