Question

Dilations, picture below.

Answer 1

• -5

Task :

• To find the scale factor (k) of the dilation.

Solution :

In order to find the scale factor of the dilation, we simply will divide the x or y coordinate of the dilated point by the respective coordinate of the original point.

• 
  `k = - \frac {25}{ 5} = - 5 \\`

Thus, the scale factor of the dilation is -5 .

Answer 2

Scale factor = -5

Explanation:

Dilation is a transformation that resizes a figure by a scale factor, causing all distances from the center of dilation to be multiplied by the same factor.

The coordinates of the preimage vertex are (3, -5).

The coordinates of the image vertex are (-15, 25).

In this case, the center of dilation is the origin (0, 0). Therefore, we can find the scale factor (k) by dividing the x- and y-coordinates of the image by the corresponding x- and y-coordinates of the preimage:

`\textsf{$x$-coordinate:}\quad k=(-15)/(3)=-5`

`\textsf{$y$-coordinate:}\quad k=(25)/(-5)=-5`

Since the scale factor is the same for both x and y, we can say that the scale factor of the dilation is k = -5.

Note that when the scale factor in a dilation is negative, it indicates that the dilation takes place in the opposite direction from the center of dilation on the same straight line containing the center and the pre-image point.