Question

1. a trapezoid with vertices a(1, 2), b(3, 2), c(4, 4), and d(0, 4) is dilated to a(0.5, 1), b(1.5, 1), c(2, 2), and d(0, 2). what is the dilation factor?

a 2
b $\frac{1}{2}$
c 1
d $\frac{3}{2}$

Explanation:

Step1: Recall dilation factor formula

The dilation factor \( k \) for a point \((x,y)\) transformed to \((x',y')\) is \( k=\frac{x'}{x}=\frac{y'}{y} \) (assuming center at origin, which is implied here as coordinates scale uniformly).

Step2: Use point A to calculate k

For point \( A(1,2) \) and \( A'(0.5,1) \):

• For x - coordinate: \( k=\frac{0.5}{1} = 0.5=\frac{1}{2} \)
• For y - coordinate: \( k=\frac{1}{2}=0.5 \)

We can verify with another point, say \( B(3,2) \) and \( B'(1.5,1) \):

• \( k=\frac{1.5}{3}=0.5=\frac{1}{2} \), \( k = \frac{1}{2}=0.5 \)

Answer:

\(\frac{1}{2}\) (corresponding to option b)