Chapter 4.8, Problem 43SPR

To determine

The type of congruence transformation.

Answer to Problem 43SPR

The transformation here is reflection, translation and rotation.

Explanation of Solution

Given:

The given figure is:

  

Calculation:

Reflection is a transformation over a line. Each point on the original figure and reflected figure are at the same distance from the line of reflection.

In given figure, each vertex of the original figure and the reflected figure are at the same distance from the line y = -x.

The transformation here is reflection.

The translation is a type of transformation in which all the parts of the object move to the same distance and in the same direction.

In the given figure, the image has just moved 2 units right and 2 units upwards.

Hence, it is also a translation.

A rotation is a type of transformation over a fixed point, at a specific angle, and in a specific direction. Each point of the original figure and the rotated figure are at the same distance from the center.

In the given figure, each vertex is at the same distance from the origin. The angles formed by each pair of corresponding points and the origin are of 180 degrees.

Thus, it is also a rotation.