Question

Figure A below is translated 4 units left and 1 unit down and then reflected over the y-axis.

On a coordinate plane, triangle A has points (5, negative 2), (5, negative 3), (2, negative 4). Triangle B has points (negative 1, negative 3), (negative 1, negative 4), (2, negative 5).

Which best explains whether figure B is the image of figure A under the specified transformations?
Figure B is not the image of figure A because the triangles are not congruent.
Figure B is not the image of figure A because the transformations were performed in an incorrect order.
There is not enough information to determine whether figure B is the image of figure A after the transformations.
Figure B is the image of figure A. The transformations were performed correctly.

Answer 1

Apply the translation then the reflection to each vertex of A.

Translate 4 left and 1 down: (x,y) -> (x-4, y-1)
- (5,-2) -> (1,-3)
- (5,-3) -> (1,-4)
- (2,-4) -> (-2,-5)

Reflect over the y-axis: (x,y) -> (-x, y)
- (1,-3) -> (-1,-3)
- (1,-4) -> (-1,-4)
- (-2,-5) -> (2,-5)

These final points match triangle B exactly, so: "Figure B is the image of figure A. The transformations were performed correctly."