Tuesday, November 27, 2012

Transformations on the Coordinate Plane

We will be talking about three transformations of figures on the coordinate plane. (you will not be responsible for these concepts on any unit test.  However, you may say this on an upcoming quiz or possible the NJASK)

Translation - a translation is simply a sliding of the figure to a different position on the coordinate plane.  THe reason why it is called a translation is because you are taking all the x-coordinates of the original figure and moving them left or right by the same number of spaces.  The same is true for the y-coordinates.

Example:  The coordinates (-7,-2), (-7,-6), and (-4,-6) form a right triangle in Quadrant III.  You can translate this triangle to Quandrant I by adding 9 (in this case) to all your x-coordinates and 10 to all your y-coordinates.  So your translated points will be (2, 8), (2, 4) and (4, 4).  Try it on grid paper to have a look.

To describe a translation you write T(x,y).  For the translation below, sliding from the red triangle to the blue, we moved five spaces to the left, so we subtracted 5 (or -5).  We also moved up 3 spaces.  Because the x axis is left to oright and the y is up and down, the translation can be written as T(-5,3).

Reflection - a reflection is a mirror image across either the x-axis or the y-axis.  Since the y-axis measures the positions of the horitzontal lines, reflecting the image across this axis means that all the y-coordinates remain the same but the oppiste of the x-coordinates are needed to reflect the figure.  The same is true for reflecting across the x-axis.  However, all the x-coordinates remain the same, but the y's change.

For the reflection above, notice that point A is (1,7).  However the reflection or A' is (-1,7).  Point B is (2,3) so the reflection across the y-axis is (-2,3).  If we were to reflect the image across the x-axis, point A (1,7) transforms into point A' (1,-7).

Rotation  - in regards to rotation the figure is turned a certain number of degrees around a specific point.  This point is call the center of rotation.  The center of rotation can be the origin or even a point one the figure.