Question

Dilation S maps the point (2, 1/2) to (3, 3/4). Write a rule that would describe the dilation S:

A) (x, y) → (x + 1, y + 1/4)
B) (x, y) → (2x, 2y)
C) (x, y) → (x + 1, y + 1/2)
D) (x, y) → (3x, 3y)

Answer 1

The rule that describes the dilation S mapping (2, 1/2) to (3, 3/4) is (x, y) → (x + 1, y + 1/4), corresponding to option A.

Step-by-step explanation:

The student's question involves finding a rule that describes the dilation S that maps the point (2, 1/2) to (3, 3/4). We can calculate the change in the x-coordinate and the y-coordinate separately. The x-coordinate has increased by 1, from 2 to 3, while the y-coordinate has increased by 1/4, from 1/2 to 3/4. Therefore, the rule representing this dilation S should account for these changes for any point (x, y).

The correct rule that describes this dilation would be (x, y) → (x + 1, y + 1/4), which corresponds to option A from the given choices. This rule adds 1 to the x-coordinate and 1/4 to the y-coordinate of any given point to produce the dilated point.