Question

If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n =

.

Answer 1

Answer: If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n = 1.

Explanation:

• A dilation is a transformation that creates an image that is the same shape as the original, but is a different size.

Since in a dilation, the corresponding the sides of the pre-image and sides of the image are proportional.

Such that ,
`\frac{\text{pre-image}}{\text{image}}=n, \text{where n is the scale factor.}`...........(1)

Let ΔABC is dilated to ΔA'B'C' such that AB≅A'B', BC≅B'C' and AC≅B'C'.

Then
`\frac{\text{pre-image}}{\text{image}}=(AB)/(A'B')=(BC)/(B'C')=(AC)/(A'C')=1`.......(2)

From (1) and (2),
`n=1`

Therefore, If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n = 1.

Answer 2

If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n = 1. Dilating an image with a dilation factor of 1 will result to the same image and that ensures the congruency between the pre-image and the dilated image.