A rectangle has vertices A(2,4), B(7,4), C(7,1), and D(2,1). Which of the following vertices could be a vertex for a similar but not congruent figure?

Rationale

B(21,12) could be a vertex for a similar but not congruent figure.

This choice represents a point that maintains the same proportional relationship to the original rectangle's dimensions but is not identical in size. Similar figures have corresponding angles equal and corresponding sides in proportion, which allows for similarity without congruence.

A (B(9,4)) YOUR ANSWER

This point is a translation of vertex B(7,4) along the x-axis by 2 units. The rectangle formed would be congruent to the original rectangle, as it retains the same dimensions and angles.

B (B(14,4)) YOUR ANSWER

Similar to the previous option, this point is also a translation, moving vertex B(7,4) along the x-axis by 7 units. The resulting figure would also be congruent to the original rectangle, maintaining its dimensions and thus failing to meet the criteria for similarity alone.

C (B(21,12)) CORRECT

This choice creates a rectangle that is similar but not congruent to the original. The dimensions of the new rectangle would be proportionally larger, as the x-coordinate and y-coordinate ratios from the original rectangle are preserved, differing in scale.

D (B(4,7)) YOUR ANSWER

This point does not maintain the proportional dimensions of the original rectangle. The distance from the x and y coordinates (2 to 4 along the x-axis and 1 to 7 along the y-axis) does not conform to the necessary ratio of the original rectangle's sides, resulting in a figure that is neither similar nor congruent.

Conclusion

In summary, for a rectangle defined by the vertices A(2,4), B(7,4), C(7,1), and D(2,1), the vertex B(21,12) allows for a similar figure due to its proportional dimensions, while the other options either result in congruent figures or fail to maintain the necessary ratios. Understanding these relationships is crucial in geometric transformations and similarity concepts.

A rectangle has vertices A(2,4), B(7,4), C(7,1), and D(2,1). Which of the following vertices could be a vertex for a similar but not congruent figure?

B(21,12) could be a vertex for a similar but not congruent figure.

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