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).

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