Answer:
When you perform translations, you slide a figure left or right, up or down. This means that on the coordinate plane, the coordinates for the vertices of the figure will change.
To graph a translation, perform the same change for each point.
You can identify a reflection by the changes in its coordinates. In a reflection, the figure flips across a line to make a mirror image of itself. Take a look at the reflection below.
Figures are usually reflected across either the
x−
or the
y−
axis. In this case, the figure is reflected across the
y−
axis. If you compare the figures in the first example vertex by vertex, you see that the
x−
coordinates change but the
y−
coordinates stay the same. This is because the reflection happens from left to right across the
y−
axis. When you reflect across the
x−
axis, the
y−
coordinates change and the
x−
coordinates stay the same. Take a look at this example.
In the figure above the coordinates for the upper-left vertex of the original figure are (-5, 5). After you reflect it across the
x−
axis, the coordinates for the corresponding vertex are (-5, -5). How about the lower-right vertex? It starts out at (-1, 1), and after the flip it is at (-1, -1). As you can see, the
x−
coordinates stay the same while the
y−
coordinates change. In fact, the
y−
coordinates all become the opposite integers of the original
y−
coordinates. This indicates that this is a vertical (up/down) reflection or a reflection over the
x−
axis.
In a horizontal (left/right) reflection or a reflection over the
y−
axis, the
x−
coordinates would become integer opposites. Let’s look at an example.
This is a reflection across the
y−
axis. Compare the points. Notice that the
y−
coordinates stay the same. The
x−
coordinates become the integer opposites of the original
x−
coordinates. Look at the top point of the triangle, for example. The coordinates of the original point are (-4, 6), and the coordinates of the new point are (4, 6). The
x−
coordinate has switched from -4 to 4.
You can recognize reflections by these changes to the
x−
and
y−
coordinates. If you reflect across the
x−
axis, the
y−
coordinates will become opposite. If you reflect across the
y−
axis, the
x−
coordinates will become opposite.
You can also use this information to graph reflections. To graph a reflection, you need to decide whether the reflection will be across the
x−
axis or the
y−
axis, and then change either the
x−
or
y−
coordinates.
