Figure a below is translated 4 units left and 1 unit down and then reflected over the y-axis. which best explains whether figure b is the image of figure a under the specified transformations? a. figure b is not the image of figure a because the triangles are not congruent. b. figure b is not the image of figure a because the transformations were performed in an incorrect order. c. there is not enough information to determine whether figure b is the image of figure a after the transformations. d. figure b is the image of figure a. the transformations were performed correctly.

D. Figure B is the image of A. The final shape and position of an object is called an image of the original one after transformation. Triangle B is congruent to Triangle A since it wasn't enlarged, or shrunk in any way. The transformation is also performed correctly as shown on the diagram.

D.Figure B is the image of figure A. The transformations were performed correctly.

Justification:

To determine and prove whether the image of the figure A is the figure A after the given transformation you can work graphycally or analitically.

To show you I will work analitically, as the graphfical method is hard to explain without a video.

So:

1) First, translatation 4 units left and 1 unit down means:

(x,y) → (x - 4, y - 1), so any point (a,b) will be transformed into point (a - 4, b - 1).

2) Second, reflection over the y-axis means:

(x,y) → (-x,y).

So, the point (a - 4, b - 1) will be transformed into point (4 - a, b - 1)

3) Check what happens with the vertices of the figure A, using the last relation (a,b)→(4 - a, b - 1).

vertex (5, -2) → (4 - 5, -2 - 1) = ( -1, -3)

vertex (5, -3) → (4 - 5, -3 - 1) = ( -1, -4)

vertex (2, - 4) → (4 - 2, -4 - 1) = (2, - 5).

As you can see in the figure, the points (-1, -3), (-1, -4), and (2, -5) are the vertices of the triangle B, which shows that the transformations yield the figure A to figure B.

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