Geometry- How to rotate a single point

Question

How to rotate point A(–3, 4) 90 ̊ clockwise about the origin, (0, 0).

Answer 1

For every 90° clockwise, (x,y) changes to (y,-x) so our new point is (4, -(-3)), better known as (4,3).

If we were to rotate it 180°, we'd do it again and our new point would be (3,-4), or (-x,-y).

270° does it yet again to (-4,-3), or (y,-x), and 360° takes us back to (-3,4).

So, you can memorize all of those, or know that each 90° is (y,-x) and keep flip flopping.

Answer 2

If the rotation were something other than 90 or 180 degrees, we might do this using a rotational matrix. However, for a 90 degree rotation, you should answer this by thinking about how we reach the original point by going up 4 and to the left 3. Rotating right 90 degrees, we go right 4, then up 3. This gets us to (4, 3). As a check, note that the inner product of (3,-4) and (4, 3) is 0..