Question 28

A quadrilateral in the coordinate plane is transformed by scaling it down.

The transformation represented by (1/2 x, 1/2 y) results in a similar figure because it scales the quadrilateral while maintaining its shape and proportions. This is a dilation transformation, which is essential for similarity.

A) (1/2 x, 1/2 y)

This option is correct because it applies a scaling transformation that reduces the size of the quadrilateral by half while preserving the angles and the relative lengths of the sides. This transformation meets the criteria for similarity, as the shape remains unchanged.

B) (2x, y + 3)

This option is incorrect because it involves a scaling transformation in the x-direction (doubling the x-coordinates) and a translation in the y-direction (adding 3 to the y-coordinates). The introduction of translation disrupts the proportional relationships necessary for similarity, making the resulting figure not similar.

C) (x + 5, y - 2)

This option is incorrect as it represents a translation of the quadrilateral by moving it 5 units to the right and 2 units down. Since there is no scaling involved, the shape and size of the original quadrilateral remain unchanged, but it does not satisfy the conditions for similarity because the overall proportions are not preserved relative to the original figure.

D) (- x - 2, y - 3)

This option is also incorrect because it combines a reflection across the y-axis (due to the negation of x) with a translation (moving down and left). While the angles may remain the same, the transformation alters the size and orientation of the shape, preventing it from being similar to the original quadrilateral.

Conclusion

The correct answer, option A, effectively scales the quadrilateral while maintaining its shape, thus resulting in a similar figure. In contrast, the other options involve translations or combinations of transformations that modify the original figure's dimensions or position, which disqualifies them from being similar.