Question

△BCD is dilated to become triangle △B′C′D′.△BCD has coordinates B(4, 2), C(6, 2), and D(6, 5).△B′C′D′ has coordinatesB′(2, 1), C′(3, 1), andD′(3, 2.5).What is the scale factor of the dilation? 0.250.524

Answer 1

Given:

Coordinates of BCD ==> B(4, 2), C(6, 2), and D(6, 5).

Coordinates of B'C'D' ==> B'(2, 1), C'(3, 1), and D'(3, 2.5)

Let's find the scale factor of the dilation.

To find the scale factor of the dilation, we can simply divide each cordinate point of the dilated figure from the corresponding coordinate point of the original figure.

We have:

$scale\text{ factor = (}\frac{B^{\prime}}{B}),(\frac{C^{\prime}}{C}),(\frac{D^{\prime}}{D})$

Since we can use any coordinate point, let's take that of B and B'.

Thus, we have:

$\begin{gathered} \text{scale factor =(}\frac{2}{4},\frac{1}{2}) \\ \\ \text{scale factor=(0.5,0.5)} \end{gathered}$

Therefore, we can say traingle BCD was dilated by a scale factor of 0.5 to become traingle B'C'D'.

ANSWER:

0.5