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How do I carry out reflections in lines?

By David Moody on the 11th of June, 2012

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    Usually the question will be in coordinate notation (a graph). If they want you to reflect across the x-axis here are the steps you need:

    1.  what are the coordinates of the line? Example: (2,3), (5,2)

    2. (x,y) becomes (x, -y) so the sample points would change to (2, -3), (5, -2)

    3. There you have it! If you need to graph your points go ahead. You should now have the line reflected across the x-axis

    If they want it reflected across the y-axis use the same steps, but for step 2 instead the rule is (x,y) becomes (-x,y)

    Another common one is reflect it over the line y=x. Again, same steps, but for step 2 the rule is (x,y) becomes (y,x)

    If you want to see this visually here is a good source:

    http://www.mathwarehouse.com/transformations/reflections-in-math.php

     

    Refine By Megan on the 17th of January, 2013

Suggested reading…

Describe fully, and carry out reflections in lines and rotations about any point

Reflection

Reflection means we take the mirror image of a shape, where the mirror would be, we call it the line of symmetry. it stays the same but changes in direction. You may find questions that will ask you for the reflection of a line.

You can use tracing paper to help reflect your shape.

 

Rotation

Every point on a rotated shape is at the same distance from the point of rotation. It stays the same size, but changes in direction.

Rotation about a point

Imagine a shape that has been cut out from some paper, and placed on the graph. If you want to rotate it about a spot, you can stick a pin where the 'spot' is, and as you spin the shape, that is rotation about a spot.

Cutting out the shape is a useful way to practice rotation, but you will not have scissors  in your exam!

Remember, every point on the rotated shape must be the same distance from the spot as the original shape.

Rotation about a centre of rotation.

Imagine the shape being turned round a point, like you are drawing a circle.

To rotate an object, again take each corner one by one and rotate it using a protractor. If the rotation is by 90o,180o,270othen we you can use the grid on the paper.

For example, if you want to rotate the point (2,3), about the origin, 90o clockwise, insteading of going right 2 steps and up 3 steps, we go down 2 steps and right 3 steps, giving you the co-ordinates (3,2)

(remember up and down give you y-coordinate, and left and right give you x co-ordinates, it doesn't matter what order it is in!)

There are no tricks to finding the centre of rotation, it is done by observing, but remember every point must be at the same distance.

 

Little Bridge

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