Question

a triangle is rotated 90° about the origin. which rule describes the transformation?
(x, y) → (-x, -y)
(x, y) → (-y, x)
(x, y) → (-y, -x)
(x, y) → (y, -x)

Explanation:

Step1: Recall rotation rules

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by the rule \((x,y)\to(-y,x)\).

Step2: Verify the rule

Let's take a simple point, say \((1,0)\). Rotating \((1,0)\) \(90^{\circ}\) counter - clockwise about the origin gives the point \((0,1)\). Using the rule \((x,y)\to(-y,x)\), when \(x = 1\) and \(y=0\), we have \((-0,1)=(0,1)\).

Answer:

\((x,y)\to(-y,x)\) (the second option)