Question

Which rule represents a dilation on the coordinate plane? (x, y) --> (y, x) (x, y) --> (-x, y) (x, y) --> (kx, ky) (x, y) --> (x, y + 2)

Answer 1

The rule that represents a dilation on the coordinate plane is (x, y) --> (kx, ky). This transformation scales a figure by a constant factor k for both coordinates.

Step-by-step explanation:

The rule that represents a dilation on the coordinate plane is (x, y) --> (kx, ky). A dilation in the coordinate plane is a transformation that scales a figure by a constant factor k, which is the same for both x- and y-coordinates. This scaling factor can be greater than 1 for an enlargement, less than 1 for a reduction, or negative to include a reflection along with the scaling.

In contrast, the rule (x, y) --> (y, x) represents a reflection across the line y=x, the rule (x, y) --> (-x, y) reflects the point across the y-axis, and the rule (x, y) --> (x, y + 2) translates the point upwards by 2 units.