Question

a polygon is shown on the coordinate plane below. the following transformations are to be performed, in order, on the polygon. - translate 4 units in a negative y - direction. - translate 6 units in a positive x - direction. - reflect about the y - axis. which of the following describes the location of vertex d after the transformations?

Explanation:

Step1: Note initial coordinates of D

The initial coordinates of vertex D are $(-6,1)$.

Step2: First translation (negative y - direction)

Subtract 4 from the y - coordinate. New coordinates are $(-6,1 - 4)=(-6,-3)$.

Step3: Second translation (positive x - direction)

Add 6 to the x - coordinate. New coordinates are $(-6 + 6,-3)=(0,-3)$.

Step4: Reflection about y - axis

Change the sign of the x - coordinate. New coordinates are $(0,-3)$ (since the x - coordinate was 0, it remains the same after reflection).

Answer:

$(0,-3)$