just change the signs of the point (3,3) to (-3,-3)
it might help to draw a rough sketch or graph. the origin is (0,0)
distance from (3,3) to (0,0) is square root of 3^2+3^2 = 3sqr2
If you found the equation of the line through (3,3) and (0,0) and then went
the same distance on the opposite side of the origin, that would be the point you want.
the equation of the line through all 3 points is y=x it has slope = 1. It's a diagonal line with angle 45 degrees with the x axis
now go the same distance along the line into the 3rd quadrant, 3sqr2
distance from (-3,-3) to the origin is 3sqr2, the same distance from the origin to (3,3)
to be symmetric about the origin, it has to be the same distance to the origin, along the same line.
But just change the sign of the x and y coordinates. That's a lot easier. Still, you feel a lot more confident with at least a rough sketch or graph, where you can visualize it.
