Question

Which transformation was applied to figure A to form figure B?

A. Figure A was translated 3 units right and 10 units down to form figure B.
B. Figure A was translated 10 units right and 3 units down to form figure B.
C. Figure A was reflected across the line m to form figure B.
D. Figure A was rotated 90° clockwise about the point N to form figure B.

Answer 1

B. Figure A was translated 10 units right and 3 units down to form figure B.

Explanation:

We are given two figures (both are squares) and we are to determine whether which transformations were applied to figure A to form figure B.

Initially, the coordinates of figure A were:

(-3, 0), (-7, 0), (-3, 4) and (-7, 4)

And the following coordinates when it transformed to figure B:

(3, 1), (7, 1), (3, -3) and (7, -3)

So basically figure A was translated 10 units right and 3 units down to form figure B.

Therefore, the correct answer option is B.

Answer 2

B

Explanation:

Let point N has coordinates (0,0), then figure A has vertices at points (-3,0), (-7,0), (-7,4) and (-3,4). Figure B has vertices at points (3,1), (7,1), (7,-3) and (3,-3).

1. Translation 10 units to the right has the rule

(x,y)→(x+10,y).

Then vertices of the figure A have images:

• (-3,0)→(7,0);
• (-7,0)→(3,0);
• (-7,4)→(3,4);
• (-3,4)→(7,4).

2. Translation 3 units down has the rule

(x,y)→(x,y-3).

Then images are

• (7,0)→(7,-3);
• (3,0)→(3,-3);
• (3,4)→(3,1);
• (7,4)→(7,1).

As you can see these points are exactly the vertices of the figure B.