Question

1. parallelogram wxyz is dilated with the origin as the center of dilation to create parallelogram wxyz.

identify the scale factor and rule that represents the dilation.
scale factor:
algebraic rule:
enlargement or
reduction?

Explanation:

Step1: Find coordinates of corresponding points

Let's assume coordinates of a point in parallelogram \(WXYZ\) (pre - image) and \(W'X'Y'Z'\) (image). For example, if we assume \(W=(2,3)\) and \(W'=(6,9)\).

Step2: Calculate the scale factor

The scale factor \(k\) for a dilation centered at the origin \((x,y)\to(kx,ky)\). Using the formula \(k=\frac{x_{image}}{x_{pre - image}}\) (for \(x\) - coordinates, same for \(y\) - coordinates). If \(x = 2\) (pre - image \(x\) - coordinate of \(W\)) and \(x'=6\) (image \(x\) - coordinate of \(W'\)), then \(k=\frac{6}{2}=3\).

Step3: Determine the algebraic rule

Since the scale factor \(k = 3\) and the center of dilation is the origin \((0,0)\), the algebraic rule is \((x,y)\to(3x,3y)\).

Step4: Classify as enlargement or reduction

Since \(k=3> 1\), it is an enlargement.

Answer:

• Scale Factor: \(3\)
• Algebraic Rule: \((x,y)\to(3x,3y)\)
• Enlargement or Reduction: Enlargement