Question

The coordinates of △ABC are (12,16), (24,36), and (20,28). If △ABC undergo a dilation with a scale factor of 0.4 centered at the origin, find the new coordinates.

• A. (48,64), (96,144), and (80,112)
• B. (4.8,6.4), (9.6,14.4), and (0.8,11.2)
• C. (4.8,6.4), (9.6,14.4), and (6,11.2)
• D. (4.8,6.4), (9.6,14.4), and (8,11.2)

Answer 1

The correct option is D (4.8,6.4), (9.6,14.4), and (8,11.2)

Given coordinates are (12,16), (24,36), and (20,28).

It is also given that scale factor is 0.4, centered at the origin.

Coordinates of the dilated images are:

$(12,16)=(12\times 0.4,16\times 0.4)=(4.8,6.4)$

$(24,36)=(24\times 0.4,36\times 0.4)=(9.6,14.4)$

$(20,28)=(20\times 0.4,28\times 0.4)=(8,11.2)$

Therefore, the new coordinates would be (4.8,6.4), (9.6,14.4), and (8,11.2).

So, Option (d) is correct.