ΔABC is dilated by a scale factor of 0.25 with the origin as the center of dilation, resulting in the image ΔA′B′C′. If A = (-1,

Question

MrMuchimi

3 years ago

11

ΔABC is dilated by a scale factor of 0.25 with the origin as the center of dilation, resulting in the image ΔA′B′C′. If A = (-1,

-5), B = (2, 1), and C = (14, 17 ), what is the length of B'C'?

Mathematics

1 answer:

Leni [432] · Answer 1 · 2022-04-23T16:17:17+03:00

Answer:

5

Step-by-step explanation:

To find B and C prime, you must multiply them by .25, or 1/4.

B' =

(-2 x .25),(1 x .25)

I did mine in fraction form, because it will prove to be more useful in future mathematics.

B' = (1/2 , 1/4)

Repeat the process with C.

C' =

(14 x .25),(17 x .25)

C' =

(7/2 , 17/4)

You only need to focus on B and C because you are finding the length of B'C'.

The formula for distance is the square root of x to the sub of 2 minus x to the sub of 1 squared minus y to the sub of 2 minus y to the sub of 1 square.

x2 - x1 = 7/2 - 1/2 = 6/2 = 3 squared = 9

y2 - y1 = 17/4 - 1/4 = 16/4 = 4 squared = 16

16 + 9 = 25

Square root of 25 is 5.

Therefore, the distance is 5.