Question

Which of these triangle pairs can be mapped to each other using two reflections?

Answer 1

Answer: The correct option is figure (1).

Explanation:

Reason for correct option:

The figure (1) shows the reflection across the side XY followed by reflection across the side YT.

When we reflect the triangle XYZ across the side XY we get the triangle XYT as shown in below figure.

After that we reflect the triangle XYT across the side YT and we get the triangle PYT.

Therefore, only figure 1 shows the triangle pairs can be mapped to each other using two reflections.

Reason for incorrect options:

The figure (2) shows the rotation of 180 degree along the point y.

The figure (3) shows the reflection across the side XY followed by the translation.

The figure (4) shows the reflection, followed by rotation , followed by translation.

Answer 2

We will see that the correct option is the pair shown in figure 1.

What is a reflection?

A reflection is a transformation that, for a defined line, reflects a figure of function across that line.

For example, if you have a circle in the first quadrant on a coordinate axis, and you reflect it along the x-axis, then the circle will now be below the x-axis, in the fourth quadrant.

With this in mind, to map th one triangle into another one, we must have two things:

• The two triangles must have the same dimensions (that we can assume is true).
• The touching vertices ( or nearest vertices) of the two triangles must be the equivalent vertex for the figures.

We can see that the only pair of triangles that meet the second condition are the ones in figure 1, where the touching vertices are the ones for the 90° angle.

Then the only correct option is the pair in figure 1.

If you want to learn more about reflections, you can read:

https://brainly.com/question/16625676