The image of a triangle after it has been dilated with a center of dilation at the origin has vertices at A prime(12, –6), B prime(–24, –12), and C prime. If the pre-image of B prime, point B, has coordinates of (–18, –9) and the pre-image of C prime, point C, has coordinates of (–13.5, 18), which statements are true? Check all that apply. The coordinates of C prime are (27, 18). The coordinates of C prime are (–18, 24). The scale factor is 1 and one-third. The scale factor is 1 and one-fifth. The scale factor is Three-fourths. The coordinates of A are (16, –8). The coordinates of A are (9, –4.5).

The true statement are; The coordinates of C prime are (–18, 24). The scale factor is 1 1/3 . The coordinates of A are (9, –4.5).

How to find if a pair of figure is not dilated version of each other?

Dilation of a figure will leave its sides get scaled (multiplied) by same number.

Thus, suppose if a rectangle is dilated, and its sides were of length = L and width = W, then its dilated version would be having length = Ln, and width = Wn where n is the factor of scaling.

At image B (-24, -12) and pre image B (-18, -9),

we can work out the scale factor by (-24/-18) and (-12/-9) both equal 4/3

Using the scale factor to go from the pre image to the image,

We can find C coordinate by pre image C by the scale factor.

C is (-13.5 x 4/3) and (18 x 4/3)

C is (-18, 24)

So, The scale factor is 4/3, which is the mixed numeral of 1 1/3.

To find the pre image of point A;

A is (12/(4/3)) and (-6/(4/3))

A is (9, - 4 1/2)

Hence, the true statement are;

The coordinates of C prime are (–18, 24).

The scale factor is 1 1/3 .

The coordinates of A are (9, –4.5).

Learn more about dilation here:

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