Question

what happens to the coordinates of a point (x, y) after a 90-degree counterclockwise rotation around the origin?
○ a. $(-y, -x)$
○ b. $(-y, x)$
○ c. $(y, -x)$
○ d. $(x, -y)$

Explanation:

To determine the coordinates of a point \((x, y)\) after a 90 - degree counterclockwise rotation about the origin, we can use the rule for such a rotation. The rule for a 90 - degree counterclockwise rotation around the origin is that the new coordinates \((x', y')\) of the point \((x, y)\) are given by \(x'=-y\) and \(y' = x\). So the new point is \((-y,x)\). We can also verify this with an example. Let's take a point, say \((1,0)\). A 90 - degree counterclockwise rotation about the origin should take it to \((0,1)\). Using the rule \((-y,x)\) where \(x = 1\) and \(y = 0\), we get \((- 0,1)=(0,1)\), which is correct. Another example: take the point \((0,1)\). A 90 - degree counterclockwise rotation about the origin should take it to \((-1,0)\). Using the rule \((-y,x)\) with \(x = 0\) and \(y = 1\), we get \((-1,0)\), which is correct.

Answer:

b. \((-y,x)\)