Question

After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y). A student determined y to be –2. Evaluate the student's answer. A. The student is correct. B. The student incorrectly calculated the scale factor to be –2. 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

B. The student incorrectly calculated the scale factor to be –2

Explanation:

Given that :

After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y).

The student determined y to be -2

If a figure dilated with a center of (0, 0) and scale factor k, then

(x , y) → (kx , ky)

(4, -6) → (12, y)

`k = (x')/(x)`

`k = (12)/(4)`

k = 3

Thus; the scale factor is 3

Now; the y-coordinate can now be calculated as;

ky = (3 × -6)

ky = -18

Therefore; the value of y = -18 and the student incorrectly calculated the scale factor to be -2.