Question

Carlos performed a transformation on trapezoid EFGH to create E’F’G’H, as shown in the figure below: what transformation did Carlos perform to create E’F’G’H? A. Translation B. Rotation C. Reflection D. Dilation

Answer 1

Carlos performed a Reflection to create E’F’G’H.

Step-by-step explanation:

The transformation from trapezoid EFGH to E’F’G’H reflects a change in orientation while maintaining the shape and size of the figure. In a reflection, each point of the original trapezoid is flipped across a line of symmetry to its corresponding point on the new trapezoid. This process results in an image that is a mirror image of the original, maintaining the same distances between the points and preserving the angles.

In this case, the figure EFGH underwent a transformation that involved flipping it over a line of symmetry, resulting in the formation of E’F’G’H. Every point on the original trapezoid found its corresponding point on the new trapezoid at an equal distance from the line of reflection, thus preserving the size and shape while reversing its orientation. A reflection is characterized by this reversal of orientation across a line, which perfectly describes the change observed from EFGH to E’F’G’H.

The nature of the transformation is evident as the image maintains congruence with the original trapezoid, aligning perfectly with the properties of a reflection. Thus, it can be confidently concluded that Carlos performed a Reflection to create E’F’G’H.

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Answer 2

A transformation that Carlos performed to create E’F’G’H include the following: B. Rotation.

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a rotation of 90° clockwise about the center (origin), the coordinates of trapezoid E’F’G’H' are as follows;

(x, y) → (y, -x)

Coordinate E (6, -4) → Coordinate E' (-4, 6)

Coordinate F (-4, -4) → Coordinate F' (-4, 4)

Coordinate G (-2, -6) → Coordinate E' (-6, 2)

Coordinate H (-7, -7) → Coordinate H' (-7, 7)

Missing information:

The question is incomplete and the missing figure is shown in the attached picture.