Question

the triangle bcd is a dilation of the triangle bcd. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Identify corresponding points

Coordinates: $B(8, -4)$, $B'(5, -2)$; $C(-8, -4)$, $C'(-4, -2)$; $D(-6, -8)$, $D'(-3, -4)$

Step2: Calculate scale factor (x-coordinate ratio)

Take $B$ and $B'$: $\frac{5 - 0}{8 - 0} = \frac{5}{8}$? No, use distance from origin or ratio of coordinates.
Simpler: $\frac{\text{Coordinate of } B'}{\text{Coordinate of } B} = \frac{-2}{-4} = \frac{1}{2}$ (using y-coordinates)

Step3: Verify with another point

Use $C$ and $C'$: $\frac{-2}{-4} = \frac{1}{2}$ (y-coordinates), or $\frac{-4}{-8} = \frac{1}{2}$ (x-coordinates)

Answer:

$\frac{1}{2}$