Question

example
alo used a single transformation to map
figure a onto its image a’. what is one
way alo could have mapped figure a
onto figure a’?
alo could have translated figure a 8 units
up to map figure a onto figure a’.

1 a. describe another single transformation that maps figure a onto figure a’ in
the example.

Explanation:

Step1: Analyze the vertical distance

The center of figure A is at \( y = - 4 \) and the center of figure \( A' \) is at \( y = 4 \). The mid - point of \( y=-4 \) and \( y = 4 \) is \( y=\frac{-4 + 4}{2}=0 \), which is the \( x \) - axis.

Step2: Determine the transformation

A reflection over the \( x \) - axis can map figure A onto figure \( A' \). For a point \( (x,y) \) in figure A, after reflection over the \( x \) - axis, the coordinates become \( (x, - y) \). If we take a point in figure A with \( y=-4 \), after reflection over the \( x \) - axis, \( y = 4 \), which matches the \( y \) - coordinate of the corresponding point in \( A' \). Also, the shape and orientation (except for the vertical flip which is consistent with reflection over \( x \) - axis) of the figure remain the same in terms of the horizontal position and the overall shape, so reflection over the \( x \) - axis is a valid single transformation.

Answer:

Alo could have reflected figure A over the \( x \) - axis to map figure A onto figure \( A' \).