Question

HELP ASAP!!!! (also image is below)

Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:

A coordinate grid is shown from negative 5 to 0 to 5 on both x -and y-axes. A polygon ABCD has A at ordered pair 1, 3, B at ordered pair 3, 4, C at ordered pair 2, 1, D at ordered pair 1, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 3, 3, B prime at ordered pair negative 5, 4, C prime at ordered pair negative 4, 1, D prime at ordered pair negative 3, 1.

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

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

Answer 1

Reflection over the y-axis followed by a translation to the left by 2 units

Explanation:

From inspection of the graph, the y-values of figure ABCD and the y-values of figure A'B'C'D' have not changed, yet the x-values have changed from positive to negative.

(x, y) → (-x, y)

This indicates a reflection in the y-axis.

To reflect figure ABCD in the y-axis, simply change the x-values to negative:

A (1, 3) → (-1, 3)

B (3, 4) → (-3, 4)

C (2, 1) → (-2, 1)

D (1, 1) → ( -1, 1)

Comparing the x-values of the figure reflected in the y-axis to the x-values of the final translated figure, the reflected figure needs to be translated to the left by 2 units.

So the total transformation is: (x, y) → (-x - 2, y)

A (1, 3) → A' (-3, 3)

B (3, 4) → B' (-5, 4)

C (2, 1) → C' (-4, 1)

D (1, 1) → D' ( -3, 1)