Question

10
what is the rule for the transformation above?
a. ( f(x,y)=(x,-y) )
b. ( f(x,y)=(y,x) )
c. ( f(x,y)=(-x,-y) )
d. ( f(x,y)=(-x,y) )

Explanation:

Step1: Analyze the transformation of \(x\) - coordinate

In the original figure and the transformed figure, for a point \((x,y)\) in the first figure, the \(x\) - coordinate remains the same. For example, if we consider a vertex of the shape. Suppose a point in the first figure has \(x=- 3\), in the second figure (after transformation) the \(x\) - coordinate of the corresponding vertex is also \(x = - 3\).

Step2: Analyze the transformation of \(y\) - coordinate

For a point \((x,y)\) in the first figure, the \(y\) - coordinate changes its sign. If a point in the first figure has \(y = 2\), the corresponding point in the second figure has \(y=-2\).

Answer:

A. \(f(x,y)=(x, - y)\)