Question

which of the following is the algebraic representation for a dilation?
(x,y)→(.5x,.4y)
(x,y)→(3x,3y)
(x,y)→(x,3y)
(x,y)→(x,y - 3)

Explanation:

Step1: Recall the formula for dilation

The algebraic representation of a dilation centered at the origin is \((x,y)\to(kx,ky)\), where \(k\) is the scale factor.

Step2: Analyze each option

• For \((x,y)\to(0.5x,0.4y)\), since \(0.5

eq0.4\), it is not a dilation (dilation requires the same scale factor for \(x\) and \(y\) coordinates).

• For \((x,y)\to(3x,3y)\), here \(k = 3\). Using the formula \((x,y)\to(kx,ky)\), this is a dilation with a scale factor of \(3\).
• For \((x,y)\to(x,3y)\), only the \(y -\)coordinate is scaled. In a dilation, both \(x\) and \(y\) coordinates should be scaled by the same non - zero factor.
• For \((x,y)\to(x,y - 3)\), this is a vertical translation (shift down by \(3\) units), not a dilation.

Answer:

\((x,y)\to(3x,3y)\)