This diagram shows a pre-image △ABC, and its image, △A′′B′′C′′, after a series of transformations. Select from the drop-down menus to correctly complete the statements. △ABC is Choose... to become △A′B′C′. Then △A′B′C′ is Choose... to become △A′′B′′C′′ . Because the transformations are Choose... , the pre-image and image are Choose... . Triangles on a coordinate plane whose axes are labeled x and y. Triangle A B C has vertex A at 1 comma negative 1, vertex B at 4 comma negative 2, and vertex C at 7 comma 2. Triangle A prime B prime C prime has vertex A prime at negative 1 comma 1, vertex B prime at negative 4 comma 2, and vertex C prime at negative 7 comma negative 2. Triangle A double prime B double prime and C double prime has vertex A double prime at negative 1 comma negative 2, vertex B double prime at negative 4 comma negative 1, and vertex C double prime at negative 7 comma negative 5.

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AFOKE88 AFOKE88 · Answer 1 · 2021-10-15T22:39:26+02:00

The answers that complete the statements of the series of transformations are;

- △ABC to △A′B′C′; because the △ABC has been rotated at angle of 180° about the origin.

- △A′B′C′ to △A′′B′′C′′; Because the △A′B′C′ has been shifted down by 3 units.

- All 3 transformations are rigid transformations

- All three transformations are congruent transformations.

The image showing triangles △ABC, △A′′B′′C′′, and △A′B′C′ is missing and so I have attached it.

From the image attached, we see the following coordinates of the triangles;

Coordinates of △ABC; A(1, -1), B(4, -2), C(7, 2)

Coordinates of △A′B′C′; A'(-1, 1), B'(-4, 2), C'(-7, -2)

Coordinates of △A′′B′′C′′; A''(-1. -2), B''(-4, -1), C''(-7, -5)

Now, in transformation from △ABC to △A′B′C′, we see that the pattern of transformation is; (x, y) → (−x ,−y). This pattern where coordinates of x and y are transformed to the negative part of them denotes that there has been a rotation at angle of 180° about the origin.

In transformation from △A′B′C′ to △A′′B′′C′′, we see that triangle shifted down because the y-coordinates have reduced by 3 units. Thus, we can say that the transformation was to shift △A′B′C′ down by 3 units.

In each of the transformations, we can tell that regardless of the position of the triangle, the distances AB, BC and AC remain the same. Thus, the transformation is rigid. The transformations are also congruent because all their corresponding sides are equal.

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