Question

parallelogram ABCD is reflected over the y axis, followed by a reflection over the x axis, and then rotated 180 degrees about the origin,. What is the location of point A after the transformations are complete? a (-5,-1) b. (5,1) c.(-5,1) d.(5,-1)

Answer 1

Answer: Option c.

Step-by-step explanation:

The missing figure is attached.

Given a point $(x,y)$:

1. If it is reflected over the y-axis:

$(x,y)$ → $(-x,y)$

2. If it is reflected over the x-axis:

$(x,y)$ → $(x,-y)$

3. If it is rotated 180 degrees about the origin:

$(x,y)$ → $(-x, -y)$

In this case, you can identify that the point A is:

$A(-5,1)$

Then:

If it is reflected over the y-axis:

$(-5,1)$ → $(5,1)$

If then it is reflected over the x-axis:

$(5,1)$ → $(5,-1)$

Finally, if this is followed by a rotationf of 180 degrees about the origin, this is:

$(5,-1)$ → $(-5,1)$