Question

I NEED HELP ASAP WILL GIVE 50 POINTS!!!

Answer 1

Answer:  The complete statement is:

ΔABC is rotated through an angle of 180° about the origin to become ΔA'B'C'. Then, ΔA'B'C' is translated 3 units down to become ΔA''B''C''. Because the transformations are ROTATION and TRANSLATION, the pre image and image are SIMILAR.

Step-by-step explanation:  We are given a diagram that shows a pre-image ΔABC and its image ΔA′′B′′C′′ after a series of transformations.

We are given to find the transformations from ΔABC to ΔA'B'C' and then from ΔA'B'C' to ΔA''B''C''.

The co-ordinates of the vertices of ΔABC are A(1, -1), B(4, -2) and C(7, 2).

The co-ordinates of the vertices of ΔA'B'C' are A'(-1, 1), B'(-4, 2) and C'(-7, -2).

The co-ordinates of the vertices of ΔA''B''C'' are A''(-1, -2), B''(-4, -1) and C''(-7, -5).

We can see that

the vertices of ΔABC follow the rule (x, y) ⇒ (-x, -y) to form the vertices of ΔA'B'C'.

So, ΔABC is rotated about the origin (0, 0) through an angle of 180° to form ΔA'B'C'.

Again, the vertices of ΔA'B'C' follow the rule (x, y) ⇒ (x, y-3) to form the vertices of ΔA''B''C''.

So, ΔA'B'C' is translated 3 units down to form ΔA''B''C''.

Thus, the required transformations are

ΔABC is rotated through an angle of 180° about the origin to become ΔA'B'C'. Then, ΔA'B'C' is translated 3 units down to become ΔA''B''C''. Because the transformations are ROTATION and TRANSLATION, the pre image and image are SIMILAR.

Answer 2

Answer:

Step-by-step explanation:

Given that triangle ABC is transformed two times to get triangle

A"B"C"

First ABC is transformed in to A'B'C' as follows:

The coordinates of A are (1,-1) and transformed into A'(-1,1)

Similarly B (4,-2) became B'(-4,2) and

C(7,-2) became C'(-7,2)

i.e. (x,y) becomes (-x,-y)

This is nothing but reflection about a point here origin.

Thus first transformation is reflection on the origin.

Next is exactly shifting 3 units down