3.2.4 practice modeling geometric sequences

Question

Mathematics: 3.2.4 practice modeling geometric sequences

PuppyLover3479 · Accepted Answer

Fourth option is correct. The length of B'C' is 1 unit.

Step-by-step explanation:

The vertices of triangle ABC are A = (2, 2), B = (4, 3), and C = (6, 3).

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$BC=\sqrt{(6-4)^2+(3-3)^2}=2$

The length of BC is 2 units.

It is given that ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image ΔA′B′C′.

It means the ΔABC and ΔA′B′C′ are similar and corresponding sides of ΔA′B′C′ and ΔABC are proportional.

$k=\frac{B'C'}{BC}$

The scale factor is 0.5.

$0.5=\frac{B'C'}{2}$

$0.5\times 2=B'C'$

1=B'C'

Therefore the length of B'C' is 1 unit and fourth option is correct.

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