Question

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'?

Answer 1

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.