Question

which notation describes this transformation?
a. $(x,y)=(-x,-y)$
b. $(x,y)=(x,-y)$
c. $(x,y)=(x - 8,y - 8)$

Explanation:

Step1: Analyze Option A

For a point \((x,y)\), \((x',y')=(-x,-y)\) represents a rotation of \(180^{\circ}\) about the origin. But looking at the figure, it is not a \(180^{\circ}\) rotation.

Step2: Analyze Option B

For a point \((x,y)\), \((x',y')=(x, - y)\) represents a reflection over the \(x -\)axis. But the figure is not a reflection over the \(x -\)axis.

Step3: Analyze Option C

Let's take a vertex of figure 1. Suppose a vertex of figure 1 is \((3,5)\). For figure 2, if we use \((x',y')=(x - 8,y - 8)\), then \(x'=3-8=-5\) and \(y'=5 - 8=-3\). If we check another vertex of figure 1, say \((6,5)\), then \(x'=6-8=-2\) and \(y'=5 - 8=-3\). This translation (shifting) rule works for the transformation from figure 1 to figure 2.

Answer:

C. \((x',y')=(x - 8,y - 8)\)