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Describe a sequence of transformations that maps figure a to figure b

Describe a sequence of transformations that maps figure a to figure b-example-1

2 Answers

7 votes

Answer:

dilate by a factor of 2

rotate CCW 90°

User Bernie Wong
by
3.7k points
4 votes

Answer:

  • rotate CCW 90°
  • dilate by a factor of 2

Explanation:

First of all, we need to discover the relation Figure B has to Figure A.

Figure B has dimensions that are twice those of Figure A, so a dilation by a scale factor of 2 will be required. The "points" of figure A are on its "south" side, while those of figure B are on its "east" side. Rotation 90° CCW will be involved.

If we consider just these two transformations, we find that they are sufficient to map A to B without any additional translation. Since both transformations use the origin as a reference, their order does not matter.

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Rotating figure A by 90° CCW moves the vertex of its "notch" from (2, 2) to (-2, 2). Dilating the rotated fibure by a factor of 2 moves its "notch" vertex to (-4, 4), as shown in Figure B.

A suitable sequence of transformations is ...

  • Rotation 90° CCW
  • Dilation by a factor of 2 about the origin

These can be done in either order.

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Additional comment

The transformations are ...

(x, y) ⇒ (-y, x) . . . . . . rotation 90° CCW

(x, y) ⇒ (2x, 2y) . . . . dilation by a factor of 2

The composition of these transformations is ...

(x, y) ⇒ (-2y, 2x)

User David Gageot
by
3.8k points