Question

a pentagon is transformed according to the rule $r_{0,180^{circ}}$. which is another way to state the transformation?
$(x,y)\to(-x,-y)$
$(x,y)\to(-y - x)$
$(x,y)\to(x,-y)$
$(x,y)\to(-x,y)$

Explanation:

Step1: Recall rotation rules

When a point \((x,y)\) is rotated \(180^{\circ}\) about the origin \((0,0)\), the new coordinates \((x',y')\) can be found using the rule \((x,y)\to(-x,-y)\).

Step2: Analyze each option

• Option 1: \((x,y)\to(-x, -y)\) is the rule for \(180^{\circ}\) rotation about the origin.
• Option 2: \((x,y)\to(-y,-x)\) is the rule for \(270^{\circ}\) clockwise (or \(90^{\circ}\) counter - clockwise) rotation about the origin.
• Option 3: \((x,y)\to(x,-y)\) is the rule for reflection over the \(x\) - axis.
• Option 4: \((x,y)\to(-x,y)\) is the rule for reflection over the \(y\) - axis.

Answer:

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