Question

one vertex of a triangle is located at (0, 5) on a coordinate grid. after a transformation, the vertex is located at (5, 0). which transformations could have taken place? select two options. $r_{0,90^{circ}}$ $r_{0,180^{circ}}$ $r_{0,270^{circ}}$ $r_{0,-90^{circ}}$ $r_{0,-180^{circ}}$

Explanation:

Step1: Recall rotation rules

• For a rotation of \(90^{\circ}\) counter - clockwise (\(R_{0,90^{\circ}}\)) about the origin, the rule is \((x,y)\to(-y,x)\). For \((0,5)\), we get \((- 5,0)\).
• For a rotation of \(180^{\circ}\) (\(R_{0,180^{\circ}}\)) about the origin, the rule is \((x,y)\to(-x,-y)\). For \((0,5)\), we get \((0, - 5)\).
• For a rotation of \(270^{\circ}\) counter - clockwise (\(R_{0,270^{\circ}}\)) about the origin (which is equivalent to \(90^{\circ}\) clockwise), the rule is \((x,y)\to(y,-x)\). For \((0,5)\), we get \((5,0)\).
• For a rotation of \(-90^{\circ}\) (which is \(270^{\circ}\) counter - clockwise), the rule is \((x,y)\to(y,-x)\). For \((0,5)\), we get \((5,0)\).
• For a rotation of \(-180^{\circ}\) (which is \(180^{\circ}\) rotation), the rule is \((x,y)\to(-x,-y)\). For \((0,5)\), we get \((0,-5)\).

Answer:

\(R_{0,270^{\circ}}\), \(R_{0,-90^{\circ}}\)