Find the prime factorization of 24. Make sure to show all of your work.
2 answers:
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Answer:
1. A. They are similar because polygon G'H'J'K' can be obtained from polygon GHJK by a sequence of transformation
2. B. Reflection across the y-axis
Step-by-step explanation:
1) The coordinates of the sides of the polygon are;
G(-6, 8), H(-2, 4), J(-4, 2), and K(-8, 2)
G'(3, -1), H'(1, -3), J'(2, -4), K'(4, -4)
The length, l, of the sides are;
Length of GH = √((8 - 4)² + ((-6) - (-2))²) = 4·√2
Length of HJ = √((2 - 4)² + ((-4) - (-2))²) = 2·√2
Length of JK = √((2 - 2)² + ((-4) - (-8))²) = 4
Length of KG = √((2 - 8)² + ((-8) - (-6))²) = 2·√10
Similarly, we have;
Length of G'H' = √(((-3) - (-1))² + (1 - 3)²) = 2·√2
Length of H'J' = √(((-3) - (-4))² + (1 - 2)²) = √2
Length of J'K' = √(((-4) - (-4))² + ((4)- 2)²) = 2
Length of K'G' = √(((-4) - (-1))² + ((4) - 3)²) = √10
Therefore, the polygon G'H'J'K' can be obtained from the polygon GHJK by scaling down by a factor of 2, and the two polygons are similar
2) Given that the coordinates of figure 2 are (-2, 3) (-3, 5), (-4, 1), and (-6, 1), while the corresponding coordinates of figure 3 are (2, 3), (3, 5), (4, 1), and (6, 1) which is equivalent to a transformation from (x, y) to (-x, y) which is the transformation involved in a reflection across the y-axis