Question

1. trapezoid efgh is dilated with the origin as the center of dilation to create trapezoid efgh. identify the scale factor and rule that represents the dilation. scale factor: algebraic rule: enlargement or reduction?

Explanation:

Step1: Identify Coordinates

Let's find coordinates of a vertex (e.g., E) and its image (E'). Assume E is at \((x_1, y_1)\) and E' at \((x_2, y_2)\). From the grid, suppose E is \((-2, 6)\) and E' is \((-4, 12)\) (or check another vertex, say F: F \((-2, -2)\), F' \((-4, -4)\)).

Step2: Calculate Scale Factor

Scale factor \(k = \frac{\text{Image Coordinate}}{\text{Original Coordinate}}\). For x - coordinate: \(k=\frac{-4}{-2}=2\) (same for y - coordinate: \(\frac{12}{6}=2\), \(\frac{-4}{-2}=2\)). So scale factor is 2.

Step3: Determine Enlargement/Reduction

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

Step4: Algebraic Rule

Dilation about origin: \((x,y)\to(kx,ky)\), so rule is \((x,y)\to(2x,2y)\).

Answer:

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