Question

After a dilation with a center of (0, 0), a point was mapped as (2, -5) → (3, y). A student determined y to be -2.5. Evaluate the student's answer.

A. The student is correct.
B. The student incorrectly calculated the scale factor as 0.5.
C. The student incorrectly divided by the scale factor instead of multiplying by it.
D. The student incorrectly added the scale factor instead of multiplying by it.

Answer 1

The student's answer is incorrect. The correct answer would be y = -10.

Step-by-step explanation:

To evaluate the student's answer, we need to determine if the point (2, -5) maps to (3, -2.5) after a dilation with a center of (0, 0).

Using the formula for dilation, we can find the scaled coordinates: (x', y') = (kx, ky), where (x, y) are the original coordinates and (x', y') are the scaled coordinates.

Plugging in the given values, we get (2, -5) → (2 * 1, -5 * 1) = (2, -5).

Therefore, the answer the student provided, y = -2.5, is incorrect. The correct answer would be y = -10.