WILL MARK BRAINLIST!! Triangle PQR is transformed to triangle P'Q'R. Triangle PQR has vertices P (3, -6), Q (0, -9), and R (-3,0). Triangle P'Q'R has vertices P' (1, -2), Q' (0,3), and R' (-1, 0). What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R? Explain your answer.

The scale factor of the dillation that transforms triangle PQR to triangle P'Q'R' is .

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There is a typographical mistake in the statement. Correct statement is:

Triangle PQR is transformed to triangle P'Q'R. Triangle PQR has vertices P (3, -6), Q (0, -9), and R (-3,0). Triangle P'Q'R has vertices P' (1, -2), Q' (0,-3), and R' (-1, 0). What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R? Explain your answer.

From Linear Algebra we define dillation with respect to a given point as:

(Eq. 1)

Where:

- Origin, dimensionless.

- Scale factor, dimensionless.

- Original point, dimensionless.

- Dilated point, dimensionless.

If we consider that and we know that , , , , and , then scale factor of each point is, respectively:

Point P

Point Q

Point R

Hence, the scale factor of the dillation that transforms triangle PQR to triangle P'Q'R' is .

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