Question

1. describe the transformation represented on hannahs graph.
2. for giovannis graph, write a \1\ and a \2\ next to the 1st and 2nd transformations in the sequence of transformations represented by his graph. not all choices will be used.

a. reflection over x - axis
b. translation 4 units right
c. rotation 180° clockwise
d. rotation 90° clockwise
e. translation 4 units left

1. for andrews graph, write a \1\ and a \2\ next to the 1st and 2nd transformations in the sequence of transformations represented by his graph. not all choices will be used.

a. dilation
b. rotation
c. translation
d. dilation
e. translate

Explanation:

Step1: Analyze Hannah's graph transformation

Observe the position - change of $\triangle ABC$ to $\triangle A'B'C'$. The shape and size remain the same, and the orientation also remains the same. The $x$ - coordinates of the vertices of $\triangle ABC$ are increased by 8 units while the $y$ - coordinates remain the same. This is a translation.

Step2: Determine the type of translation

The translation is 8 units to the right.

Step1: Analyze the first - stage transformation

For $\triangle DEF$ to $\triangle D'E'F'$, the orientation of the triangle has changed. If we consider the center of rotation at the origin, a $90^{\circ}$ clock - wise rotation can be identified.

Step2: Analyze the second - stage transformation

From $\triangle D'E'F'$ to $\triangle D''E''F''$, the $x$ - coordinates of the vertices of $\triangle D'E'F'$ are increased by 4 units while the $y$ - coordinates remain the same. This is a translation 4 units right.

Answer:

1. Translation 8 units right

For Giovanni's graph: