Question

question
what is the image point of (-3, -8) after the transformation $r_{y=-x} \circ r_{180^\circ}$?
answer attempt 1 out of 2

Explanation:

Step1: Apply \( R_{180^\circ} \) to \((-3, -8)\)

The rule for a \( 180^\circ \) rotation (\( R_{180^\circ} \)) about the origin is \((x, y) \to (-x, -y)\). So for \((-3, -8)\), we get \((-(-3), -(-8))=(3, 8)\).

Step2: Apply \( r_{y = -x} \) to \((3, 8)\)

The rule for reflection over the line \( y=-x \) (\( r_{y=-x} \)) is \((x, y) \to (-y, -x)\). Applying this to \((3, 8)\), we get \((-8, -3)\).

Answer:

\((-8, -3)\)