Question

write the algebraic description that maps cdefg onto cdefg.

Explanation:

Step1: Find the horizontal translation

Take a point, say \(C(-1,3)\) and \(C'(3,1)\). The \(x -\)coordinate changes from \(-1\) to \(3\). The formula for horizontal translation is \(x'=x + h\), where \(h\) is the horizontal shift. So, \(3=-1 + h\), then \(h = 4\).

Step2: Find the vertical translation

Using the same points \(C(-1,3)\) and \(C'(3,1)\). The formula for vertical translation is \(y'=y + k\). So, \(1 = 3 + k\), then \(k=-2\).

The general rule for translation is \((x,y)\to(x + 4,y-2)\)

Answer:

\((x,y)\to(x + 4,y - 2)\)