Question

Which description of a figure and its image matches the transformation described by (x, y) → (x, 3y)?

A) The figure is a rectangle, and its image is a stretched rectangle with a length three times that of the original.
B) The figure is a square, and its image is a square with three times the area.
C) The figure is a circle, and its image is an elongated ellipse with a major axis three times the length of the minor axis.
D) The figure is an isosceles triangle, and its image is a scaled-up isosceles triangle with a base three times longer.

Answer 1

The transformation (x, y) → (x, 3y) represents a vertical stretch by a scale factor of 3.

Step-by-step explanation:

The given transformation (x, y) → (x, 3y) is a vertical stretch by a scale factor of 3. This means that the y-coordinate of each point in the figure is multiplied by 3 to get the corresponding point in the image.

A) The description of a stretched rectangle with a length three times that of the original matches the transformation described by (x, y) → (x, 3y).

Therefore, the correct answer is A) The figure is a rectangle, and its image is a stretched rectangle with a length three times that of the original.