Question

answer the questions about figure a and figure b below. (a) are figure a and figure b congruent? yes no (b) which sequence(s) of transformations will map figure a onto figure b exactly? choose all that apply. translate figure a to the left 7 units, and then rotate that result counterclockwise ( 90^{circ} ) about the origin. reflect figure a over the y - axis, and then rotate that result counterclockwise ( 90^{circ} ) about the origin. reflect figure a over the y - axis, and then translate that result down 6 units. rotate figure a counterclockwise ( 90^{circ} ) about the origin, and then translate that result down 7 units. none of these

Explanation:

(a)

Congruent figures have the same shape and size. By visual inspection, Figure A and Figure B have the same shape and size.

(b)

• Option 1: Translating left \(7\) units and rotating counter - clockwise \(90^{\circ}\) about the origin does not map Figure A to Figure B.
• Option 2: Reflecting over the \(y\) - axis and then rotating counter - clockwise \(90^{\circ}\) about the origin does not map Figure A to Figure B.
• Option 3: Reflecting over the \(y\) - axis and then translating down \(6\) units maps Figure A to Figure B.

Let's assume a point \((x,y)\) in Figure A. After reflection over the \(y\) - axis, the point becomes \((-x,y)\). Then after translation down \(6\) units, the point becomes \((-x,y - 6)\) which is the correct transformation.

• Option 4: Rotating counter - clockwise \(90^{\circ}\) about the origin (\((x,y)\to(-y,x)\)) and then translating down \(7\) units (\((-y,x-7)\)) does not map Figure A to Figure B.

Answer:

(a) Yes
(b) Reflect Figure A over the \(y\) - axis, and then translate that result down \(6\) units.