Question

triangle abc is rotated to create the image abc. which rule describes the transformation? (x,y)→(x,−y) (x,y)→(y,x) (x,y)→(−x,−y) (x,y)→(−y,−x)

Explanation:

Step1: Assume a point in triangle \(ABC\)

Let's take point \(B(1, - 1)\) in \(\triangle ABC\). Its image in \(\triangle A'B'C'\) is \(B'( - 1,1)\)

Step2: Check each transformation rule

• For the rule \((x,y)\to(x, - y)\): If \(x = 1,y=-1\), then \((1,-(-1))=(1,1)

eq(-1,1)\)

• For the rule \((x,y)\to(y,x)\): If \(x = 1,y =-1\), then \((-1,1)\)
• For the rule \((x,y)\to(-x,-y)\): If \(x = 1,y=-1\), then \((-1,1)\)
• For the rule \((x,y)\to(-y,-x)\): If \(x = 1,y=-1\), then \((1,-1)

eq(-1,1)\)

Let's take another point \(A(-1,-1)\) in \(\triangle ABC\). Its image in \(\triangle A'B'C'\) is \(A'(1,1)\)

• For the rule \((x,y)\to(y,x)\): If \(x=-1,y =-1\), then \((-1,-1)\)
• For the rule \((x,y)\to(-x,-y)\): If \(x=-1,y=-1\), then \((1,1)\)

Answer:

\((x,y)\to(-x,-y)\)