Question

How are the original coordinates related to the coordinates after the translation?

Answer 1

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.