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

1. the image is multiplied by the scale factor. if the scale factor is 2, the image is twice the size of the preimage. if the scale factor is ⅓, the image is one third the size. only a scale factor of 1 preserves congruency

Answer 2

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

Step-by-step explanation:

• A dilation is a transformation that produces an image that is similar as the original, but has a different size. In a dilation, the corresponding the sides of the pre-image and sides of the image are proportional.

$\Rightarrow\frac{\text{pre-image}}{\text{image}}=n (\text{scale factor})$

Let ΔPQR is dilated to ΔP'Q'R' such that ΔPQR≅ΔP'Q'R'

By CPCTC, PQ=P'Q'  QR≅Q'R' and PR≅P'R'.

$\Rightarrow\frac{PQ}{P'Q'}=\frac{QR}{Q'R'}=\frac{PR}{P'R'}=1$

⇒ n=1

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