Question

en el plano de coordenadas, abcd es un rectángulo del origen, care... y un polígono pqrs, que se transforma en la... coordenadas. 28. ¿cuál es el factor de escala de la dilatación? o a: 1, porque pqrs - ad es 3 o b: 1, porque m∠... / m∠... = 1 o c: 2, porque pq/ab = ad/dc = 2 o d: 4, porque sb - dc = 4

Explanation:

To solve this problem about the scale factor of a dilation, we analyze each option:

Option A:

Says the scale factor is 1 because \( PAGS - AD = 3 \). This reasoning is illogical (subtraction doesn’t relate to dilation scale factor, which involves ratios of lengths, not differences). Eliminate A.

Option B:

Claims the scale factor is 1 because \( \frac{m\angle A'B'C'}{m\angle ABC} = \frac{m\angle B'C'D'}{m\angle BCD} = 1 \). Dilation preserves angle measures (angles remain equal), but the scale factor of a dilation is about the ratio of corresponding side lengths, not angle measures. Equal angles do not imply a scale factor of 1 (they just confirm similarity, not the specific scale). Eliminate B.

Option C:

States the scale factor is 2 because \( \frac{PQRS}{AB} = \frac{QR}{DC} = 2 \). Dilation scale factor is the ratio of the length of a side in the image (\( PQRS \) or \( QR \)) to the length of the corresponding side in the original figure (\( AB \) or \( DC \)). If \( \frac{\text{image side}}{\text{original side}} = 2 \), this matches the definition of a scale factor of 2.

Option D:

Says the scale factor is 4 because \( SB - DC = 4 \). Again, dilation scale factor involves ratios of lengths, not differences. Subtraction is irrelevant here. Eliminate D.

Answer:

C. 2, porque \( \frac{PQRS}{AB} = \frac{QR}{DC} = 2 \)