The transformation R_(y-axis)∘ R_(x-axis)(△ ABC) can be written as R_(y-axis)(R_(x-axis)(△ ABC)). This means that △ ABC will be reflected in the x-axis and then the image will be reflected in the y-axis.
A''(-2,-2), B''(1,-1), C''(-1,1)
Practice makes perfect
The transformation R_(y-axis)∘ R_(x-axis)(△ ABC) can be written as R_(y-axis)(R_(x-axis)(△ ABC)). This means that △ ABC will be reflected in the x-axis and then the image will be reflected in the y-axis.
First, we will reflect the point A(2,2) across the x-axis. To do this, let's begin by plotting the point and drawing the line of reflection. Also, we will draw a line that is perpendicular to the line of reflection that passes through A(2,2). An detailed explanation on how to draw a perpendicular line through a point is given here.
Then, we can measure the distance from the preimage point to the line of reflection and locate the reflected image the same distance from the given line on the opposite side.
As we can see, A'(2,- 2) is the point after the reflection across the x-axis. We can repeat the previous steps to find B' and C'.
We will now connect the points in order to draw △ A'B'C', which is the image of △ ABC after a reflection across the x-axis.
The coordinates of the vertices after the first reflection are A'(2,-2), B'(-1,-1), and C'(1,1).
Reflection Across the y-axis
We will now repeat the same procedure as before. This time to reflect △ A'B'C' in the y-axis.
Finally, we will connect the points in order to draw △ A''B''C'', which is the image of △ ABC after the two reflections.
The coordinates of the vertices after the two reflections are A''(-2,-2), B''(1,-1), and C''(-1,1).
