Question

In the figure, polygon ABCD is transformed to create polygon A′B′C′D′.

This transformation is a____ by a factor of_____ .

Answer 1

horizontal stretch by a factor of 2

Answer 2

Answer: This transformation is a horizontal stretch by the factor 2.

Step-by-step explanation: Since, according to the given figure, vertices of square ABCD are:

A≡(3,0) B≡(1,0) C≡(1,2) and D≡(3,2)

Here After the transformation of square ABCD we get a rectangle A′B′C′D′.

whose vertices are, A'≡(6,0) B'≡(2,0), C'≡(2,2) and D'≡(6,2) (Here A', B', C' and D' are transformed from points A, B , C and D respectively.)

Since, in horizontal stretch by a factor k the point (x,y) in a graph f(x) is transformed to the (kx,y).

And after seeing the coordinates of vertices of square ABCD and rectangle A′B′C′D′, it is clear that there is no change in the y-coordinates in all the vertices of both square ABCD and rectangle A′B′C′D'. Moreover, the x-coordinates are increasing by multiplying 2. Therefore it is a horizontal stretch by factor 2.