Question

A certain mapping in the xy plane has the following property: Each point P with coordinates (x,y) is mapped to a point P'with coordinates (x-5, y-2).
Which one of the following statements is true?A. The property defines a reflection.B. The property defines a rotation.C. The property defines a translation.

Answer 1

Answer:

C.The property defines a translation

Step-by-step explanation:

We are given that a certain mapping in the xy-plane

Each point P (x,y) is mapped to a point P'(x-5,y-2).

We have to find that which statement is true in given option.

It is not reflection property because reflection about any axis  then the coordinate does not change only sign of x and y change depend upon the reflection about x- axis or y- axis.

Therefore,option A is false.

Rotation:it is a transformation that turns a figure about  a fixed point called center of rotation.

Rotation can be 90 degrees , 180,270 and 360 degrees

If the point P rotate 90 degrees then the point P'(-y,x),If point P rotate about 180 degrees then the point P'(-x,-y), when the point P rotate about 270 degrees then the point P'(y,-x), when the point P rotate about 360 degrees then the point P'(x,y).

Therefore, it is not a rotation.

It is a translation property because in translation every  point must move same distance.