a The line x=a is a vertical line. When points are reflected on a vertical line, the y-coordinates do not change. Only the x-coordinates are affected.
The only figure that matches the above is figure 2.
b The line y=b is a horizontal line. When points are reflected on a horizontal line, the x-coordinates do not change. Only the y-coordinates are affected.
The only figure that matches the above is figure 4.
c When a point (a,b) is reflected in the line y=x, its image is (b,a). Let's reflect the triangle in y=x and see if we can identify any of the figures.
The only figure that matches this look is figure 1.
d A glide reflection is a translation followed by a reflection parallel to the direction of the translation. We already established that figures 1, 2, and 4 represent different reflections of figure A, leaving us figure 3 to analyze. Apart from the vertical location, we see that figure 3 resembles the shape of figure 2, which arose from reflecting figure A in the line x=a.
So far, we know that we need to perform a reflection on a vertical line. If the reflection is going to be parallel to the direction of the translation, the translation has to be either up or down. We have already established that figure 3 is below figure 2, which means that we have to translate figure A down to make it line up with figure 3.
We can conclude that figure 3 represents a glide reflection.
