A triangle has been moved 3 units left and 2 units down to form a new congruent triangle. If one original vertex was (-3,5), which of the following could be the corresponding vertex?

Rationale

The corresponding vertex after moving the original vertex (-3, 5) is (-6, 3).

To find the new position of the vertex after the transformations, we subtract 3 from the x-coordinate and 2 from the y-coordinate of the original vertex. This results in the new coordinates of (-6, 3), confirming that this point is congruent to the original vertex after the specified transformations.

A ((-6,7)) YOUR ANSWER

This point has the same x-coordinate as the correct answer but an incorrect y-coordinate. The y-coordinate of 7 does not correspond to the transformation of moving 2 units down from the original y-coordinate of 5, which should yield a y-coordinate of 3.

B ((0,3)) YOUR ANSWER

While this point has the correct y-coordinate of 3, the x-coordinate of 0 does not reflect the required transformation. Moving 3 units left from the original x-coordinate of -3 results in an x-coordinate of -6, not 0.

C ((-6,3)) CORRECT

This point correctly reflects the transformation applied to the original vertex. By moving 3 units left from -3, we reach -6, and moving 2 units down from 5 results in a y-coordinate of 3, making this the correct corresponding vertex.

D ((5,7)) YOUR ANSWER

This point is incorrect as both the x-coordinate and y-coordinate do not match the transformations. Moving left from -3 should yield a negative x-coordinate, and moving down from 5 should yield a lower y-coordinate than 7, making this option not viable.

Conclusion

In summary, the transformation applied to the vertex (-3, 5) results in the coordinates (-6, 3) after moving 3 units left and 2 units down. The other choices either miscalculate the necessary transformations or provide coordinates that do not correspond to the original vertex. Correctly identifying the transformations is essential for determining congruent vertices in geometric figures.

A triangle has been moved 3 units left and 2 units down to form a new congruent triangle. If one original vertex was (-3,5), which of the following could be the corresponding vertex?

The corresponding vertex after moving the original vertex (-3, 5) is (-6, 3).

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