Question

1. rectangle klmn is dilated with the origin as the center of dilation to create rectangle klmn. identify the scale factor and rule that represents the dilation.

scale factor:
algebraic rule:
enlargement or
reduction?
enlargement

Explanation:

Step1: Determine the scale factor

Let's take a side - length. For example, if we consider the horizontal side of the rectangle. Suppose the length of a side of rectangle \(KLMN\) (original) is \(2\) units (from \(x = 0\) to \(x = 2\) for a horizontal side). The length of the corresponding side of rectangle \(K'L'M'N'\) (dilated) is \(4\) units (from \(x=- 2\) to \(x = 2\)).
The scale factor \(k\) is given by the formula \(k=\frac{\text{length of dilated side}}{\text{length of original side}}\)
\(k = 2\) since \(\frac{4}{2}=2\)

Step2: Determine if it is an enlargement or reduction

Since the scale factor \(k = 2>1\), it is an enlargement.

Step3: Determine the algebraic rule

The general rule for dilation with center at the origin \((x,y)\to(kx,ky)\). Since \(k = 2\), the rule is \((x,y)\to(2x,2y)\)

Answer:

• Scale Factor: \(2\)
• Enlargement or Reduction: Enlargement
• Algebraic Rule: \((x,y)\to(2x,2y)\)