Question

answer the questions about figure a and figure b below
(a) which sequence(s) of transformations will map figure a onto figure b exactly? choose all that apply.
translate figure a up 5 units, and then dilate that result with scale factor 2 centered at the origin.
rotate figure a counterclockwise 90° about the origin, and then dilate that result with scale factor 2 centered at the origin.
dilate figure a with scale factor 2 centered at the origin, and then translate that result up 8 units.
dilate figure a with scale factor 2 centered at the origin, and then reflect that result over the y - axis.
none of these
(b) are figure a and figure b similar?
yes no

Explanation:

Part (a)

Step 1: Analyze each transformation option

• Option 1: Translate up 5, then dilate (scale 2)

Translating Figure A up 5 units moves it closer vertically. Dilating (scaling) by 2 from the origin would then enlarge it. Visually, this aligns with Figure B’s position and size.

• Option 2: Rotate 90° counterclockwise, then dilate

Rotating 90° would change the orientation, but Figure B has the same orientation as A (just larger and higher). So rotation is unnecessary.

• Option 3: Dilate first, then translate up 8

Dilating first (scale 2) enlarges A, but translating up 8 units would overshoot Figure B’s vertical position (needs ~5 units up after dilation, not 8).

• Option 4: Dilate, then reflect over y - axis

Reflecting over y - axis would flip horizontally, but Figure B is not a horizontal flip of A.

Step 2: Confirm the correct option

Only the first option (Translate up 5, then dilate scale 2) maps A to B exactly. The other options fail due to orientation (rotation), incorrect translation distance, or reflection.

Similar figures have the same shape (proportional sides, equal angles) and can be mapped via similarity transformations (dilation, translation, rotation, reflection). Here, Figure B is a dilation (scale 2) and translation of Figure A, so they have the same shape (proportional sides, congruent angles). Thus, they are similar.

Answer:

(a):

• Translate Figure A up 5 units, and then dilate that result with scale factor 2 centered at the origin.

Part (b)