Question

if the scale factor of a dilation is less than one and greater than zero, what happens to the resulting image?
a. the resulting image will be an enlargement of the original image.
b. the resulting image will be a reduction of the original image.
c. the resulting image will be a rotation of the original image.
d. the resulting image will be a translation of the original image.

Explanation:

When the scale factor \(k\) of a dilation satisfies \(0 < k<1\), each coordinate of the original image is multiplied by \(k\). For example, if a point \((x,y)\) in the original image is dilated with scale factor \(k\), the new point is \((kx,ky)\). Since \(k\) is between \(0\) and \(1\), \(kx0,y > 0\); the same principle applies for non - positive \(x\) and \(y\) values in terms of magnitude). Rotation involves turning an image around a point (measured in degrees), and translation involves sliding an image (no multiplication of coordinates by a non - one scale factor). Enlargement occurs when \(k>1\).

Answer:

B. The resulting image will be a reduction of the original image.