myalani2015
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Trapezoid GHIJ is located in the coordinate plane at points
G(0,0),H(−1,2),I(3,2),and J(2,0).
Three transformation scenarios are described.

1. Reflect GHIJ in the x-axis and then reflect that image in the y-axis.

2. Rotate GHIJ 90º counterclockwise about the origin and then translate that image 2 units up.

3. Dilate GHIJ by a scale factor of
1
2
centered about the origin and then translate that image 2 units to the left.

Which transformation(s) produce an image that is congruent to the given figure?


Number 1 only

Number 1 only

Numbers 1 and 2

Numbers 1 and 2

Numbers 2 and 3

Numbers 2 and 3

Numbers 1, 2, and 3

Numbers 1, 2, and 3

Sagot :

A rigid transformation is one in which the distance between pairs of points

are preserved, and the image and preimage have the same dimensions.

  • The transformations that will produce an image that is congruent to the given figure is; Number 1 and 2.

Reasons:

The vertices of the trapezoid GHIZ are G(0, 0), H(-1, 2), I(3, 2), and J(2, 0)

The given transformations are;

1. GHIJ is reflected in the x-axis and the image is reflected in the y-axis

The above transformation is a double reflection.

2. GHIJ is rotated about the origin 90° counterclockwise. The resulting

image is translated up 2 units.

3. GHIJ is dilated by a scale factor of [tex]\mathbf{\frac{1}{2}}[/tex], with the center of dilation at the

origin. The resulting image is translated 2 units left.

Required:

The transformations that produce an image that is congruent to the given figure:

Solution:

Two figures are congruent if they have the same size and shape.

With the given figure being the trapezoid GHIJ, we have that a

transformation that will give an image that is congruent to the preimage

which is the trapezoid GHIJ is a rigid transformation.

Rigid transformations are;

  • Reflection
  • Rotation
  • Translation

The combinations of transformation given within the scenario that consists

of only rigid transformations are scenario 1 and scenario 2.

Therefore, the correct option is; Numbers 1 and 2.

Learn more about rigid transformation here:

https://brainly.com/question/1801406

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