A composition of transformations is a list of transformations that are performed one after the other. For example, we might first translate a shape in some direction, then rotate that shape about the origin. The first transformation is the translation, the second transformation is the rotation, and the composition is the combination of the two.
The order of transformations is important.
This is the case for compositions in general, although there are some special compositions for which the order does not matter.
The given triangle is to undergo two transformations.
First, plot the triangle that results from reflecting the given triangle across the x-axis.
Now translate the reflected triangle 4 units to the right.
The point A\left(6,\,-1\right) is first rotated 180\degree about the origin, and then it is reflected across the x-axis. This produces the point A'.
What are the coordinates of A'?
Which of the following transformations also takes A to A'?
Points A\left(-5,-7\right), B\left(4,4\right), and C\left(9,1\right) are the vertices of a triangle. What are the coordinates of A', B', and C' that result from reflecting the triangle across the y-axis, and translating it 3 units right and 5 units up?
A composition of transformations is a list of transformations that are performed one after the other. The order that you perform the transformations can effect the result.