Hi!
If we imagine the image of the point on a coordinate grid, we see that it is in the upper right grid, or Quadrant one. If a 90 degree clockwise rotation (I'm assuming around the origin) had been performed, what we want to do to find the pre-image is rotate it 90 degrees counterclockwise.
First, I would figure out what quadrant the pre-image is in. If it's rotated to the left, by 90 degrees, it moves one quadrant to the left, as it's rotated by 90 degrees, and a full rotation around 4 quadrants would be 360.
If it moves one to the left, then the new quadrant it is in is quadrant 2, or the upper left one. Since it's in quadrant 2, we can now figure out if the dimensions are negative or positive. Since it's on the negative side of the x axis, but the positive of the y, then the x coordinate will be negative and the y positive.
Now to figure out the actual coordinates. Here's how I like to imagine rotating it.
Hold your right arm up, and imagine that your hand is the point. Then rotate it to the left so it's lays flat. That's essentially what we're doing, we're taking a point that's taller on the right, and then rotating it. You'll notice that your hand was higher, but closer to the center, but once you rotated it, became a lot lower, but further away from the center.
That's the same concept here. So basically, you cannot just switch the negative positive signs of the coordinates, you actually have to flip the coordinates around themselves.
So if you take (2, 7), and you swap them, you get (7, 2). Now, the last step, is to change the negative positive of the x coordinate, to get (-7, 2).
Hope this helped!
