Question

After a dilation with a center of (0, 0), a point was mapped as (1, 4) → (4, y). A student determined y to be 16. Evaluate the student's answer.

A) The student is correct.
B) The student incorrectly calculated the scale factor to be 4.
C) The student incorrectly multiplied by the scale factor instead of adding it.
D) The student incorrectly added the scale factor instead of multiplying by it.

Answer 1

The student calculated the y-coordinate after a dilation by identifying a scale factor of 4. Applying this scale factor correctly to the original y-coordinate gives us 4 × 4 = 16, so the student's answer is correct (option A).

Step-by-step explanation:

The student mapped a point after a dilation with a center of (0, 0) from (1, 4) to (4, y). To determine if the student's calculation of y as 16 is correct, we should first identify the scale factor used in the dilation. This can be found by looking at the x-coordinates of the before and after points. The original x-coordinate of the point was 1, and it became 4 after the dilation, indicating a scale factor of 4 (since 1 × 4 = 4).

Now, we apply the same scale factor to the y-coordinate. The original y-coordinate is 4, so after the dilation, the new y-coordinate should be 4 × 4 = 16. Therefore, the student is correct.