Question

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

Explanation:

Step1: Identify coordinates of a point

Let's take point \(A(2,5)\). After transformation, its image \(A'(5, - 2)\).

Step2: Check each rule

• For the rule \((x,y)\to(y, - x)\):

If \(x = 2\) and \(y = 5\), then \(y=5\) and \(-x=-2\), so \((2,5)\to(5,-2)\)

• For the rule \((x,y)\to(-y,x)\): If \(x = 2\) and \(y = 5\), then \(-y=-5\) and \(x = 2\), so \((2,5)\to(-5,2)\)
• For the rule \((x,y)\to(-x,-y)\): If \(x = 2\) and \(y = 5\), then \(-x=-2\) and \(-y=-5\), so \((2,5)\to(-2,-5)\)
• For the rule \((x,y)\to(x,-y)\): If \(x = 2\) and \(y = 5\), then \(x = 2\) and \(-y=-5\), so \((2,5)\to(2,-5)\)

Answer:

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