Please help me on geometry transformation and pls explain why it is the correct answer

If I'm doing this correctly, the answer should be reflected over the y-axis and rotated 180°.

I originally wanted to say just reflect it over the x-axis but that's not an option, so the best alternative is this answer.

Step-by-step explanation:

The image is in Quadrant II. When you reflect the image, you're essentially flipping the image over a line to get a mirror version of that image. Y-axis reflections are actually horizontal flips over the y-axis, and X-axis reflections are actually vertical flips over the x-axis.

So with a y-axis reflection, you'll get this:

(see the uploaded image. I've color-coded A, B, C, and D to make it easier to see.)

Now because it's a perfect mirror image in Quadrant I, rotating it about the origin 180° (or two quadrants if that's easier to understand, since the image is only in one quadrant) will have it land in Quadrant III with all the points in their correct positions.

Just to clarify: a rotation is usually about the origin (0,0) when a specific point isn't referred to, and you're essentially putting a pen or pencil on the origin, then lifting a corner of the graph up and turning it around however many degrees and in whatever direction is specified. So if you're rotating a shape about the origin 90 degrees clockwise and the shape starts in Quadrant I, the positive x-axis becomes the negative y-axis, the positive y-axis becomes the positive x-axis, (2, 3) becomes (3, -2), and so on. 180-degree rotations can be done clockwise or counterclockwise, as they'll end up in the same place.

Hope this helps!

10 miles

step-by-step explanation: