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?

Explanation:

Step1: Find coordinates of K and K'

Let's assume grid has 1 unit per square. From graph, \( K = (-4, 2) \), \( K' = (-8, 4) \).

Step2: Calculate scale factor

Scale factor \( k \) is \( \frac{x'}{x} = \frac{-8}{-4} = 2 \) (or \( \frac{y'}{y} = \frac{4}{2} = 2 \)).

Step3: Determine algebraic rule

For dilation about origin, rule is \( (x, y) \to (kx, ky) \). With \( k = 2 \), rule is \( (x, y) \to (2x, 2y) \).

Step4: Check enlargement/reduction

Since \( k = 2 > 1 \), it's enlargement.

Answer:

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