Question

Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.

R (1, 1)
S (3, 1)
T (1, 6) R' (–1, –1)
S' (–3, –1)
T' (–1, –6)
Which best describes the transformation?

The transformation was a 90° rotation about the origin.
The transformation was a 180° rotation about the origin.
The transformation was a 270° rotation about the origin.
The transformation was a 360° rotation about the origin.

Answer 1

b

Explanation:

Answer 2

Correct answer is:

The transformation was a 180° rotation about the origin.

Explanation:

Given the triangle RST formed by points:

`R (1, 1),\\S (3, 1)\ and\\T (1, 6)`

is transformed using (x, y) → (–x, –y) such that coordinates of triangle R'S'T' :

`R' (-1, -1),\\S' (-3, -1)\ and\\T' (-1, -6)`

Please refer to the attached image for the given dimensions and coordinates.

It is clearly visible that:

The given triangle RST has coordinates in first quadrant.

and the resulting coordinates R'S'T' are in third quadrant.

The rotation of angle from 1st quadrant to 2nd quadrant is
`90^\circ` and

The rotation of angle from 2nd quadrant to 3rd quadrant is
`90^\circ`.

`\therefore` total rotation is
`180^\circ`.