Question

1. a triangle with vertices a(1, 2), b(2, 4), and c(3, 6) is dilated to create a(2, 4), b(4, 8), and c(6, 12). what is the dilation factor?

a. 2
b. \\(\frac{2}{3}\\)
c. \\(\frac{1}{2}\\)
d. 3

Explanation:

Step1: Recall Dilation Factor Formula

The dilation factor \( k \) is found by dividing the coordinates of the dilated point by the original point. For a point \( (x,y) \) dilated to \( (x',y') \), \( k=\frac{x'}{x}=\frac{y'}{y} \).

Step2: Apply to Point A

Take point \( A(1,2) \) and its image \( A'(2,4) \). Calculate \( k \) using \( x \)-coordinates: \( k = \frac{2}{1}=2 \). Check with \( y \)-coordinates: \( \frac{4}{2}=2 \).

Step3: Verify with Other Points (Optional)

For \( B(2,4) \) and \( B'(4,8) \): \( \frac{4}{2}=2 \), \( \frac{8}{4}=2 \). For \( C(3,6) \) and \( C'(6,12) \): \( \frac{6}{3}=2 \), \( \frac{12}{6}=2 \). All confirm \( k = 2 \).

Answer:

a. 2