Question

The vertices of a rectangle are given in the columns of the matrix [0, 0], [3, 0], [3, 3], [0, 3]. If you perform a transformation, what are the coordinates of the transformed rectangle?

a) [0, 0], [0, -3], [-3, -3], [-3, 0]
b) [0, 0], [0, 3], [3, 3], [3, 0]
c) [0, 0], [0, 3], [-3, -3], [-3, 0]
d) [0, 0], [0, 3], [-3, 3], [-3, 0]

Answer 1

Option (a) represents a reflection transformation of the rectangle across both axes from the original coordinates, while the other options do not match typical transformations, are the same as original, or do not seem to result from the same transformation.

Step-by-step explanation:

To determine the coordinates of the transformed rectangle, we need more information about the type of transformation. However, we can analyze the given options to see if any of them represent typical transformations like rotation or reflection from the original coordinates [0, 0], [3, 0], [3, 3], [0, 3].

• Option (a) suggests a reflection over the x-axis followed by a reflection over the y-axis.
• Option (b) is the same as the original rectangle's coordinates, so no transformation occurred here.
• Option (c) seems incorrect because the points are not all resulting from the same transformation.
• Option (d) suggests a 90 degree rotation counterclockwise about the origin, followed by a reflection over the x-axis.

Without having a specified transformation, option (a) [0, 0], [0, -3], [-3, -3], [-3, 0] is the only set that results from a combination of simple transformations applied to the original rectangle.