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: Find the scale factor

Let's assume a side - length. For example, if we consider the vertical side of the trapezoid. Suppose the length of \(HG\) (original) and \(H'G'\) (image).
Let the coordinates of \(H=(-6,8)\) and \(G=(-6, - 2)\), so \(HG=\vert8-( - 2)\vert = 10\). The coordinates of \(H'=(-3,6)\) and \(G'=(-3,1)\), so \(H'G'=\vert6 - 1\vert=5\).
The scale factor \(k=\frac{\text{length of image segment}}{\text{length of original segment}}\). So \(k=\frac{5}{10}=\frac{1}{2}\)

Step2: Determine enlargement or reduction

Since the scale factor \(k = \frac{1}{2}<1\), it is a reduction.

Step3: Find the algebraic rule

The algebraic rule for a dilation with center at the origin \((x,y)\to(kx,ky)\). Since \(k=\frac{1}{2}\), the rule is \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\)

Answer:

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