Question

triangle efg and triangle efg are given on the coordinate plane below. which sequence of transformations below shows that triangle efg is similar to triangle efg? ○a. triangle efg was dilated with a center of dilation at vertex e, reflected about side eg, and translated two units down and four units to the right to create triangle efg. ○b. triangle efg was dilated with a center of dilation at vertex g, reflected about side eg, and translated two units down and four units to the right to create triangle efg. ○c. triangle efg is not similar to triangle efg. ○d. triangle efg was translated two units down and four units to the right, dilated with a center of dilation at vertex e, and reflected about side ef to create triangle efg.

Explanation:

Step1: Analyze the dilation center

If we consider the dilation, looking at the relative positions of the vertices, the center of dilation should be at vertex \(G\). If we assume a dilation from \(\triangle EFG\) to \(\triangle E'F'G'\), the distances from \(G\) to other vertices in \(\triangle EFG\) and from \(G'\) (which is the image of \(G\) after reflection and translation, but since dilation is a similarity transformation that changes size while keeping shape and relative positions from the center of dilation, and in the coordinate - plane, if we consider the scaling factor, the center of dilation is \(G\).

Step2: Analyze the reflection and translation

After dilation with center \(G\), reflecting about side \(EG\) (which is a line of symmetry for the transformation in terms of orientation change) and then translating two units down and four units to the right (by comparing the coordinates of non - invariant (after dilation and reflection) vertices like \(E\) and \(E'\), \(F\) and \(F'\)).

Answer:

B. Triangle EFG was dilated with a center of dilation at vertex G, reflected about side EG, and translated two units down and four units to the right to create triangle E'F'G'.