Question

Identify the transformations represented by the following coordinate changes:

1.(x, y) → (-x, y)
2.(x, y) → (0.2x, 0.2y)
3.(x, y) → (x - 6, y + 6)

Answer 1

The coordinate changes represent a reflection over the y-axis, a uniform scaling by a factor of 0.2, and a translation 6 units to the left and 6 units upward.

Step-by-step explanation:

The transformations represented by the given coordinate changes are:

1. (x, y) → (-x, y) indicates a reflection over the y-axis as the x-coordinate is negated while the y-coordinate remains unchanged. This represents a transformation that flips the points horizontally to the left side of the coordinate system.
2. (x, y) → (0.2x, 0.2y) suggests a scaling transformation with a factor of 0.2, shrinking the figure by a factor of five both horizontally and vertically.
3. (x, y) → (x - 6, y + 6) is a translation transformation that moves points 6 units horizontally to the left side and 6 units vertically upward in the coordinate system.

These transformations manipulate the position and size of geometric figures on a two-dimensional coordinate system.