Question

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

Explanation:

Step1: Find the coordinates of a pair of corresponding points

Let's take point \(A\) and \(A'\). Suppose \(A=(x,y)\) and \(A'=(x',y')\). From the graph, assume \(A=(6,7)\) and \(A'=(3, 4)\) (approximate coordinate - reading from the grid).

Step2: Calculate the scale factor \(k\)

The formula for the scale factor \(k\) of a dilation centered at the origin \((x,y)\to(kx,ky)\). For the \(x\) - coordinate: \(k=\frac{x'}{x}\) (or for the \(y\) - coordinate \(k = \frac{y'}{y}\)). If \(x = 6\) and \(x'=3\), then \(k=\frac{3}{6}=\frac{1}{2}\).

Answer:

Scale Factor: \(\frac{1}{2}\), Enlargement or Reduction: Reduction, Algebraic Rule: \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\)