Question

A composition of transformations is given by the rule that maps (x, y) to (-x -1, y). Describe the composition of transformations that maps ABCDEF onto A"B"C"D"E"F.

a) A reflection over the y-axis followed by a translation 1 unit to the left.
b) A reflection over the x-axis followed by a translation 1 unit to the right.
c) A reflection over the y-axis followed by a translation 1 unit to the right.
d) A reflection over the x-axis followed by a translation 1 unit to the left.

Answer 1

The composition of transformations that maps ABCDEF onto A"B"C"D"E"F" is a reflection over the y-axis followed by a translation 1 unit to the right.

Step-by-step explanation:

The composition of transformations that maps points (x, y) to (-x -1, y) consists of two specific transformations. First, there is reflection over the y-axis, which changes (x, y) to (-x, y). The second transformation is a translation 1 unit to the left in the coordinate system, changing (-x, y) to (-x - 1, y).

This sequence of transformations reflects an object across the y-axis and then moves every point of the object 1 unit to the left horizontally. This is captured in the option (a): "A reflection over the y-axis followed by a translation 1 unit to the left."

The composition of transformations that maps ABCDEF onto A"B"C"D"E"F" is option c) A reflection over the y-axis followed by a translation 1 unit to the right.

When you reflect a shape over the y-axis, the x-coordinates of the points are negated. In this case, the rule (x, y) to (-x - 1, y) reflects the shape over the y-axis. Then, a translation 1 unit to the right is applied to the reflected shape.

So, the correct composition of transformations is a reflection over the y-axis followed by a translation 1 unit to the right.