Officer Aptitude Rating (OAR) Formulas Practice Test

Under a scaling transformation with factor k = 3, what is the image of the point (2, -4)?

(2, -4) (6, -12) (0, 0) (3, -8)

Correct Answer:

(6, -12)

Explanation:

In a scaling transformation with factor 3 about the origin, each coordinate is multiplied by 3. So the point (2, -4) maps to (3·2, 3·(-4)) = (6, -12). The other options don’t come from a uniform scale by 3: staying the same would need a scale factor of 1; (3, -8) would require multiplying x and y by different amounts; and (0, 0) would require the original point to be at the origin or the scale factor to be 0.

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