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

r (1, 1) r' (–1, –1)
s (3, 1) s' (–3, –1)
t (1, 6) 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.

The transformation was a 180° rotation about the origin.

Explanation:

1) These are the rules for rotation transformations:

i) Rotation 90° counter clockwise: (x,y) → (y, -x)

ii) Rotation 180° either counter clockwise or clockwise: (x,y) → (-x, -y); note that this is equivalent to a reflection across the x-axys followed by a reflection across the y-axis.

iii) Rotation 270° counter clockwise: (x,y) → (y, -x)

iv) Rotation 360° either counter clockwise or clockwise: (x,y) → (x,y); note thas this means that the image is the same preimage.

2) Conclusion:

The given rule (x, y) → (–x, –y), transformed the vertices of the triangles in this way:

R (1, 1) → R' (–1, –1)

S (3, 1) → S' (–3, –1)

T (1, 6) → T' (–1, –6)

which is the same that a reflection across the x-axys followed by a reflection across the y-axys and corresponds to the a 180° rotation about the origin.

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9