Question

Geometry - Unit 2 Readiness Assessment

Answer 1

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;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

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