A sequence is defined recursively by the formula f(n + 1) = –2f(n). The first term of the sequence is –1.5. What is the next ter
1 answer:
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Answer:
The sequence of transformations applied to shape I is:
a. reflection across the x-axis, followed by a reflection across the y-axis, and then a dilation by a scale factor of 0.5
Step-by-step explanation:
- Let us consider a point a (2,1) in shape I .
Now when this point is reflected across x-axis the point is transformed to:
(2,-1)
( Since the rule of transformation is:
(x,y) → (x,-y) )
Now again when this point is reflected across the y-axis the point is transformed to:
(-2,-1)
( Since the rule of transformation is:
(x,y) → (-x,y) )
Now when this point is dilated by a scale factor of 0.5 the point that is obtained is:
(-1,-0.5)
( Since, the rule of transformation is:
(x,y) → (0.5x,0.5y) )
Hence, A (2,1) → A' (-1,-0.5)
- Similarly we will consider one more point on the shape I i.e. B(3,1)
Now when this point is reflected across x-axis the point is transformed to:
(3,-1)
( Since the rule of transformation is:
(x,y) → (x,-y) )
Now again when this point is reflected across the y-axis the point is transformed to:
(-3,-1)
( Since the rule of transformation is:
(x,y) → (-x,y) )
Now when this point is dilated by a scale factor of 0.5 the point that is obtained is:
(-1.5,-0.5)
( Since, the rule of transformation is:
(x,y) → (0.5x,0.5y) )
Hence, B (3,1) → B' (-1.5,-0.5)
Similarly all the other points of shape I could be mapped to obtain the shape II.
Hence, option: a is correct.
