Respuesta :
Answer:
- scale factor is 2/3.
- coordinates of B are (9,-27).
- coordinates of C' are : (12,18)
Step-by-step explanation:
The image of a triangle after it has been dilated with a center at the origin has vertices at A’(-12,6) B’(6,-18) and C’ .
Point A has coordinates of (-18,9) and the pre- image of C' point C has coordinates of (18,12).
Clearly when we compare point A and point A' we see that the transformation is a dilation.
let the scale factor of dilation is 'k'.
i.e. A→ A'
i.e. k(-18,9)=(-12,6)
(-18k,9k)=(-12,6)
i.e. -18k=-12
and 9k=6
Hence, on solving we get:
k=2/3
i.e. the scale factor is 2/3.
Also,
we find the coordinates of B(c,d) by:
2/3(c,d)=(6,-18) since B→ B'
2/3×c=6
Hence c=9
and 2/3 ×d=-18
d=-27.
Hence, the coordinates of B are (9,-27).
Also the coordinates of C are (18,12)
Hence, coordinates of C' are:
[tex](\dfrac{2}{3}\times 18,\dfrac{3}{2}\times 12)\\\\=(12,18)[/tex]
Hence, the coordinates of C' are : (12,18)
The scale factor is 2/3 and the coordinates of B are (9,-27) and this can be determined by using the concept of the scale factor.
Given :
The image of a triangle after it has been dilated with a center at the origin has vertices at A’(-12,6) B’(6,-18) and C’ if the pre-image of Point A has coordinates of (-18,9) and the pre-image of point C has coordinates of (18,12).
The following steps can be used in order to determine the correct statement:
Step 1 - According to the given data, point A'(-12,6) has pre-image A(-18,9).
Step 2 - The scale factor is given by:
A [tex]\to[/tex] A'
A(-18K,9K) [tex]\to[/tex] A'(-12,6)
where K is the scale factor.
Now, the value of K is given by:
-18K = -12
k = 2/3
Step 3 - Now, the coordinates of point B is given by:
[tex]x = \dfrac{6\times 3}{2}= 9[/tex]
[tex]y = \dfrac{-18\times 3}{2}=-27[/tex]
So, the correct statement is given by options D) and E).
For more information, refer to the link given below:
https://brainly.com/question/22312172
