Question

a transformation of rectangle lmno results in rectangle lmno. which transformation maps the pre - image to the image? dilation stretch reflection rotation

Explanation:

Step1: Analyze dilation

Dilation is a transformation that changes the size of a figure. The length of \(LM = 8\) and the length of \(L'M'=6\). The ratio of the side - lengths is \(\frac{6}{8}=\frac{3}{4}\). The width of the original rectangle \(LO = 4\) and the width of the new rectangle \(L'O' = 4\). But dilation changes all side - lengths proportionally. However, in a dilation, if we consider the horizontal side - length change, we can check the properties. A dilation is a similarity transformation that scales the figure.

Step2: Analyze stretch

A stretch is not a standard rigid or similarity transformation in the sense of basic geometric transformations. A stretch usually changes the shape in a non - proportional way (e.g., horizontal stretch \(y = f(kx)\) for \(k
eq1\) changes the \(x\) - values non - proportionally with respect to \(y\) - values in a coordinate - based transformation). But in our case, if we assume a center of dilation, a dilation (a type of similarity transformation) is more appropriate as it is a transformation that changes the size of a figure by a scale factor.

Step3: Analyze reflection

A reflection is a transformation that flips a figure over a line (the line of reflection). It does not change the size of the figure. The original rectangle \(LMNO\) has side - lengths \(8\) and \(4\), and the image \(L'M'N'O'\) has side - lengths \(6\) and \(4\). Since the size (at least one side - length) has changed, reflection is not the transformation.

Step4: Analyze rotation

A rotation is a transformation that turns a figure around a point (the center of rotation). It does not change the size of the figure. Since the side - length \(LM
eq L'M'\), rotation is not the transformation.

Answer:

dilation