Question

Which algebraic representation shows a reduction?

(x, y) → (-3x, y)

(x, y) → (x - 3, y - 3)

(x, y) → (-3x, -3y)

(x, y) → (12 x, 12 y)

Answer 1

D. (x, y) →[TeX](\frac{1}{2}x,\frac{1}{2}y)[/TeX]

Explanation:

A dilation is a transformation which reproduces an image of the same shape as the original, but might be of a different size.

When the dilation produces a smaller image is called a reduction.

Mathematically, a reduction occurs whenever the scale factor is between 0 and 1.

Out of the options, the only one that has a scale factor less than one is:

(x, y) →[TeX](\frac{1}{2}x,\frac{1}{2}y)[/TeX]

Since the scale factor is 1/2 which is less than 1.

All other options are not reductions.