Transformations on the
Coordinate Plane

 

You have learned various transformation techniques.
Now you get the opportunity to experience them.

In the GeoGebra window to the right, there is a triangle. You can move the vertices of the triangle,
(points A, B, and C)
to any location you choose. Your task will then be to perform transformations as described. The image will be
a triangular polygon formed by
points A', B', and C'.

 

 

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To reflect a point over the
x-axis,
multiply the
y-coordinate
by -1.

 

 

 

 

 

 

 

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To reflect a point over the
y-axis,
multiply the
x-coordinate
by -1.

 

 

 

 

 

 

 

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To translate a point by an
ordered pair,
(a, b),
add a to the x-coordinate
and
add b to the y-coordinate.

 

 

 

 

 

 

 

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To dilate a figure by a
scale factor k
multiply both coordinates by k .

If k>1
the figure is enlarged.

If 0<k<1
the figure is reduced.

 

 

 

 

 

 

 

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To rotate a figure 90°
counterclockwise about the origin,
switch the coordinates of each point and then multiply the new
first coordinate by -1.

 

 

 

 

 

 

 

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To rotate a figure 180°
about the origin,
multiply both coordinates
of each point by -1.