Question

parallelogram abcd is rotated to create image abcd
which rule describes the transformation?
$(x,y)\to(y,-x)$
$(x,y)\to(-y,x)$
$(x,y)\to(-x,-y)$
$(x,y)\to(x,-y)$

Explanation:

Step1: Find coordinates of a point

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

Step2: Check the transformation rule

For a general point \((x,y)\), if \(x = 2,y = 5\), then for the rule \((x,y)\to(-x,-y)\), we have \((2,5)\to(-2,-5)\).
Let's check another point. Take point \(B(5,4)\). Using the rule \((x,y)\to(-x,-y)\), we get \((5,4)\to(-5,-4)\) which matches the transformation of point \(B\) to \(B'\) in the parallelogram.

Answer:

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