Which of these triangle pairs can be mapped to each other using a translation and a rotation about point a?

 The answer is the first and the third figure, attached.

Step-by-step explanation:  We are given four figures each having two triangles.

We are to select the correct pair of triangles that can be mapped to each other using a translation and a rotation about point A.

The correct figures are attached herewith.

We can see in both the figures that if we rotate triangle RAQ about the point A and then translated to the left, then it will map onto the triangle PKL.

Also, point A will map to point L, point R will map to point P and point Q will map to point K.  

Thus, the correct option is the first and third figure and it is attached.

The Figure 1 and Figure 4 are correct as these triangle pairs can be mapped to each other using a translation and rotation about point A.

Further explanation:

Translation can be defined as to move the function to a certain displacement. If the points of a line or any objects are moved in the same direction it is a translation.

Rotation is defined as a movement around its own axis. A circular movement is a rotation.

Explanation:

The angle KPL is equal to the angle ARQ.

The angle PLK is equal to the angle QAR.

The side PL is equal to the side RA.

In Figure 1 the triangle ARQ and LPK can be mapped to each other using a translation and a rotation about point A.

In Figure 2 the triangle ARQ and LPK cannot be mapped to each other using a translation and a rotation about point A.

In Figure 3 the triangle ARQ and LPK cannot be mapped to each other using a translation and a rotation about point A.

In Figure 4 the triangle ARQ and LPK can be mapped to each other using a translation and a rotation about point A.

The Figure 1 and Figure 4 are correct as these triangle pairs can be mapped to each other using a translation and rotation about point A

Learn more:

1. Learn more about inverse of the functionhttps://link.

2. Learn more about equation of circle link.

3. Learn more about range and domain of the function link

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: rotation, translation, triangle, rotation about point A, mapped, triangle pair, mapping, equal angles, sides