# Which single transformation that would have the same result as the two transformations (a) rotation by #180^@# about origin and (b) reflection in #y#-axis?

##### 2 Answers

The single transformation that would have the same result as the two transformations is the one transforming **reflection of shape in #x#-axis** .

The

#### Explanation:

Rotation by

(

When reflected in the

(

Hence, the single transformation that would have the same result as the two transformations is the one transforming

which is nothing but reflection of shape in the

(

The

#### Explanation:

The two transformations can be described using transformation matrices.

The matrix for a rotation of 180° about the origin is

This has the effect of changing the signs of the

The matrix for a reflection in the

This has the effect of changing the signs of the

If both transformations take place, the final result is given by:

The effect of this matrix is to keep the