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What Are the Key Properties of Translation in Geometric Transformations?

Translation is an important idea in geometry, especially for Year 8 math. It basically means moving a shape from one spot to another without changing how it looks or its size. Let's break down the main points about translation:

  1. Direction and Distance: Translation has a direction and a distance. We use something called a vector to show this. For example, if we move a triangle 5 steps to the right and 3 steps up, we can say it's moved by the vector (5,3)(5, 3).

  2. Shape and Size Stay the Same: When we translate a shape, it doesn’t get bigger or smaller. If we take a rectangle that's 4 cm long and 2 cm wide and move it, it will still be 4 cm by 2 cm; it just ends up in a different place.

  3. Keeping Lines Parallel: After we move a shape, all the lines that were straight stay straight. For example, if we have a square called ABCD and we translate it, then the sides AB and CD will still be parallel, and so will the sides AD and BC.

  4. Changing Coordinates: It’s easy to figure out the new spot of a point. If we have a point (x,y)(x, y) and we move it by (a,b)(a, b), its new position will be (x+a,y+b)(x+a, y+b).

In short, translation helps us move shapes around without changing them, which is really important in geometry!

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What Are the Key Properties of Translation in Geometric Transformations?

Translation is an important idea in geometry, especially for Year 8 math. It basically means moving a shape from one spot to another without changing how it looks or its size. Let's break down the main points about translation:

  1. Direction and Distance: Translation has a direction and a distance. We use something called a vector to show this. For example, if we move a triangle 5 steps to the right and 3 steps up, we can say it's moved by the vector (5,3)(5, 3).

  2. Shape and Size Stay the Same: When we translate a shape, it doesn’t get bigger or smaller. If we take a rectangle that's 4 cm long and 2 cm wide and move it, it will still be 4 cm by 2 cm; it just ends up in a different place.

  3. Keeping Lines Parallel: After we move a shape, all the lines that were straight stay straight. For example, if we have a square called ABCD and we translate it, then the sides AB and CD will still be parallel, and so will the sides AD and BC.

  4. Changing Coordinates: It’s easy to figure out the new spot of a point. If we have a point (x,y)(x, y) and we move it by (a,b)(a, b), its new position will be (x+a,y+b)(x+a, y+b).

In short, translation helps us move shapes around without changing them, which is really important in geometry!

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