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 a ‘point ahas coordinates of (-18,9) and the pre- image of c point c has coordinates of (18,12) which statements are true ? check all that apply •the coordinates of c are (27,18) •the coordinates for c are (12,8) •the scale factor is 1.5 •the scale factor is 0.75 •the scale factor is 2/3 •the coordinates of b are (9,-27) •the coordinates of b are (4,-12)

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:

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 A'

A(-18K,9K) 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:

So, the correct statement is given by options D) and E).

For more information, refer to the link given below:

link

d) 48

step-by-step explanation:

16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,272,288,304,320,336

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: