Question

Figure ABCD is transformed to A’B’C’D’, as shown:

A coordinate plane is shown. Figure ABCD has vertices A at 3 comma 1, B at 3 comma 4, C at 5 comma 5 and D at 5 comma 3. Figure A prime B prime C prime D prime has vertices A prime at negative 5 comma 1, B prime at negative 5 comma 4, C prime at negative 7 comma 5 and D prime at negative 7 comma 3.

Which of the following sequences of transformations is used to obtain figure A’B’C’D’ from ABCD?


Reflection about the x-axis followed by a translation right by 2 units
Reflection about the y-axis followed by a translation left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units

Answer 1

Based on the picture, I'd say answer B. is correct. Reflection about the y-axis followed by a translation left by 2 units.

Answer 2

Reflection about the y-axis followed by a translation left by 2 units.

Explanation:

As in rotation, reflection and translation the transformed image is congruent to the original figure(i.e all the points undergo same change), so analyzing any one point will give the series of transformation undertaken.

Taking point A(3, 1) into consideration.

Reflecting a point (x, y) over y axis, it becomes (-x, y).

Hence, reflecting A(3, 1) over y axis the new coordinates will be (-3, 1)

Again, translating a point (x, y) k units left, it becomes (x-k, y).

Hence, translating point (-3, 1) 2 units left, the new coordinates will be (-5, 1)

This is the coordinates for A'.

Hence, ABCD is reflected about the y-axis followed by a translation left by 2 units.