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Geometry - Unit 2 Readiness Assessment
This assessment is to identify your current math knowledge. Do not worry if you do not know all of the
answers. Please try to answer every question.
1.
Which best describes the relationship between polygon GHJK and polygon G'H'J'K?
A. They are similar because polygon G'H'J'K' can
be obtained from polygon GHJK by a sequence
of transformations.
B. They are similar because the area of polygon
G'H'J'K' is the same as the area of polygon
GHJK.
C. They are NOT similar because polygon
G'H'J'K' cannot be obtained from polygon
GHJK in a single transformation.
KA
D. They are NOT similar because the orientation of
polygon G'H'J'K' is not the same as the
orientation of polyon GHIK

Geometry Unit 2 Readiness Assessment This assessment is to identify your current math knowledge Do not worry if you do not know all of the answers Please try to class=

Respuesta :

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;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

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

Both the polygons are similar because polygon G'H'J'K' can  be obtained from polygon GHJK by a sequence  of transformations.

Given :

  • Polygon GHJK and polygon G'H'J'K'.
  • Coordinates  -- G(-6,8), H(-2,4), J(-4,2), K(-8,2), G'(3,-1), H'(1,-3), J'(2,-4), and K'(4,-4).

The distance formula can be used in order to determine the length of segments of the given polygon.

[tex]\rm GH=\sqrt{(-2+6)^2+(4-8)^2} =\sqrt{32}[/tex]

[tex]\rm HJ=\sqrt{(-4+2)^2+(2-4)^2} =\sqrt{8}[/tex]

[tex]\rm JK=\sqrt{(-8+4)^2+(2-2)^2} =\sqrt{16}=4[/tex]

[tex]\rm GK=\sqrt{(-8+6)^2+(2-8)^2} =\sqrt{40}[/tex]

[tex]\rm G'H'=\sqrt{(1-3)^2+(-3+1)^2} =\sqrt{8}[/tex]

[tex]\rm H'J'=\sqrt{(2-1)^2+(-4+3)^2} =\sqrt{2}[/tex]

[tex]\rm J'K'=\sqrt{(4-2)^2+(-4+4)^2} =\sqrt{4}=2[/tex]

[tex]\rm G'K'=\sqrt{(-4+1)^2+(4-3)^2} =\sqrt{10}[/tex]

Therefore, the correct option is A) They are similar because polygon G'H'J'K' can  be obtained from polygon GHJK by a sequence  of transformations.

For more information, refer to the link given below:

https://brainly.com/question/17756657

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