Question

the dashed figure is the image of the solid figure. what is the algebraic

Explanation:

Step1: Identify key - point changes

Let a point \((x,y)\) on the solid figure. Observe the transformation to the corresponding point on the dashed - figure.
For example, if we take a vertex of the solid figure say \((3, - 2)\) and its corresponding vertex on the dashed figure say \((-4,4)\).

Step2: Find the translation rule

To get from \(x = 3\) to \(x=-4\), we subtract \(7\) from the \(x\) - coordinate (\(3-7=-4\)). To get from \(y = - 2\) to \(y = 4\), we add \(6\) to the \(y\) - coordinate (\(-2 + 6=4\)).
The algebraic rule for the transformation is \((x,y)\to(x - 7,y + 6)\).

Answer:

\((x,y)\to(x - 7,y + 6)\)