Question

1. quadrilateral abcd is transformed to create quadrilateral abcd.

verbal description:
algebraic rule:

Explanation:

Step1: Find the transformation rule

Let's take a point, say \(A(-6,6)\) and \(A'(-6,-1)\). The \(x -\)coordinate remains the same (\(x=-6\) for both \(A\) and \(A'\)), and the \(y -\)coordinate changes from \(y = 6\) to \(y=-1\). The change in \(y\) is \(y'=y - 7\) (since \(6-7=-1\)).
Let's check another point: \(B(-1,4)\) and \(B'(-1,-3)\). Using the rule \(y'=y - 7\), \(4-7=-3\).

Step2: Write the algebraic rule

For a point \((x,y)\) in quadrilateral \(ABCD\), the algebraic rule for the transformation to get the corresponding point \((x',y')\) in quadrilateral \(A'B'C'D'\) is \((x,y)\to(x,y - 7)\)

Step3: Write the verbal description

Since the \(x -\)coordinate does not change and the \(y -\)coordinate is decreased by \(7\) for each point, the verbal description is: Quadrilateral \(ABCD\) is translated \(7\) units down.

Answer:

• Algebraic Rule: \((x,y)\to(x,y - 7)\)
• Verbal Description: Quadrilateral \(ABCD\) is translated \(7\) units down.