Next, let’s investigate reflections across the x-axis.

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Transmographer  

1. Use your notes to record the initial coordinates of the green point, yellow point, cyan point, and black point.
2. In the Reflect box, check “across y = 0”. A reflection across the line y = 0 is really a reflection across the x-axis.
3. Click the Reflect button.
4. Record the new coordinates of each point.
5. How did the value of the coordinates change?
   Interactive popup. Assistance may be required.

   Check Your Answer

   The x-coordinate remained the same, but the y-coordinate was transformed into its opposite.
6. How was the size and shape of the figure affected?
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   Check Your Answer

   The size and shape did not change.
7. Repeat this process using different polygons.
8. In general, how are the x and y-coordinates affected when a figure is reflected across the x-axis?
   Interactive popup. Assistance may be required.

   Check Your Answer

   When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.

You can write the rule for reflections across the x-axis in symbolic language.

P(x, y) → P^t(x, −y) or r_x−axis(x, y) = (x, −y)

In general, how are the size and shape of a figure affected a figure is reflected across the x-axis?

Interactive popup. Assistance may be required.

Check Your Answer

The size and shape did not change.

Since the size and shape of figures are not affected when a figure is reflected across the x-axis, we say reflections across the x-axis are congruence transformations.

Next, let’s investigate reflections across the line y = x.

1. Use your notes to record the initial coordinates of the green point, yellow point, cyan point, and black point.
2. In the Reflect box, check “across y = x”. Across y = x means a reflection across the line y = x.
3. Click the Reflect button.
4. Record the new coordinates of each point.
5. How did the value of the coordinates change?
   Interactive popup. Assistance may be required.

   Check Your Answer

   The x-coordinate and the y-coordinate change places.
6. How was the size and shape of the figure affected?
   Interactive popup. Assistance may be required.

   Check Your Answer

   The size and shape did not change.
7. Repeat this process using different polygons.
8. In general, how are the x and y-coordinates affected when a figure is reflected across the line y = x?
   Interactive popup. Assistance may be required.

   Check Your Answer

   When you reflect a point across the line y = x, the x-coordinate and the y-coordinate change places.

You can write the rule for reflections across the line y = x in symbolic language.

P(x, y) → P^t(y, x) or r_{y = x}(x, y) = (y, x)

In general, how are the size and shape of a figure affected when a figure is reflected across the line y = x?

Interactive popup. Assistance may be required.

Check Your Answer

The size and shape did not change.

Since the size and shape of figures are not affected when a figure is reflected across the line y = x, we say reflections across the line y = x are congruence transformations.