Question

what is the image of the point (4, −1) after a dilation with a scale factor 3 centered at the origin?
a. (3, −12)
b. (1.33, −0.33)
c. (4, −1)
d. (12, −3)

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale factor \( k \), the image of a point \( (x, y) \) is \( (kx, ky) \).

Step2: Apply the formula

Given the point \( (4, -1) \) and scale factor \( k = 3 \), we calculate the new coordinates:
\( x' = 4\times3 = 12 \)
\( y' = -1\times3 = -3 \)

Answer:

d. \( (12, -3) \)