Question

which transformation of (x, y) is a dilation? (a) a (x + 3, y + 3) b (3x, 3y) c (-x, 3y) d (3x, y)

Explanation:

Step1: Recall Dilation Definition

Dilation transforms a point \((x,y)\) by multiplying both \(x\) and \(y\) by a scale factor \(k\), resulting in \((kx,ky)\).

Step2: Analyze Option A

Option A: \((x + 3, y + 3)\) is a translation (shifting 3 units right and 3 units up), not dilation.

Step3: Analyze Option B

Option B: \((3x, 3y)\) multiplies both \(x\) and \(y\) by 3 (scale factor 3), matching dilation definition.

Step4: Analyze Option C

Option C: \((-x, 3y)\) reflects \(x\) and scales \(y\), not pure dilation (involves reflection).

Step5: Analyze Option D

Option D: \((3x, y)\) scales \(x\) but not \(y\), not a dilation (unequal scaling).

Answer:

B. \((3x, 3y)\)