Congruent Figures Practice

Question

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Question
Use the image to answer the question.

A coordinate plane with 4 quadrants shows x and y axes ranging from negative 5 to 5 in increments of 1. Three triangles are formed by joining three plotted points each. Two of the triangles are joined by connecting their vertices with rays. The coordinates of the plotted points for the triangle in quadrant 4 are left parenthesis 1 comma negative 1 right parenthesis, left parenthesis 1 comma negative 3 right parenthesis, and left parenthesis 3 comma negative 2 right parenthesis. The coordinates for the triangle in quadrant 2 are left parenthesis negative 4 comma 2 right parenthesis, left parenthesis negative 2 comma 2 right parenthesis, and left parenthesis negative 3 comma 4 right parenthesis. The side joining point left parenthesis negative 4 comma 2 right parenthesis and point left parenthesis negative 2 comma 2 right parenthesis is labeled e. The side joining point left parenthesis negative 4 comma 2 right parenthesis and point left parenthesis negative 3 comma 4 right parenthesis is labeled g. The side joining point left parenthesis negative 3 comma 4 right parenthesis and point left parenthesis negative 2 comma 2 right parenthesis is labeled h. The coordinates of the plotted points for the triangle in quadrant 1 are left parenthesis 1 comma 1 right parenthesis, left parenthesis 3 comma 1 right parenthesis, and left parenthesis 2 comma 3 right parenthesis. Three rays join each vertex of the triangle in quadrant 1 to the complementary vertices of the triangle in quadrant 2. A ray connects point left parenthesis 1 comma 1 right parenthesis to point left parenthesis negative 4 comma 2 right parenthesis. A ray connects point left parenthesis 3 comma 1 right parenthesis to point left parenthesis negative 2 comma 2 right parenthesis. A ray connects point left parenthesis 2 comma 3 right parenthesis to point left parenthesis negative 3 comma 4 right parenthesis. The arrow heads are on the vertices of the triangle in quadrant 2.

What two transformations are shown to demonstrate that the triangles are congruent?

(1 point)
rotation of
degrees counterclockwise and translation of (
)

Answer 1

The two transformations shown to demonstrate that the triangles are congruent are a rotation of 180 degrees counterclockwise and a translation of (6, -2).

Answer 2

nope

Answer 3

I apologize for the wrong answer. Based on the given information, the two transformations shown to demonstrate that the triangles are congruent are a reflection and a translation.

Specifically, the triangles in quadrant 4 and quadrant 2 are congruent because they have the same shape and size. The reflection is observed in the line of symmetry, which is the y-axis. The triangle in quadrant 4 is reflected across the y-axis to create the triangle in quadrant 2.

Additionally, there is a translation involved where the entire triangle in quadrant 2 is shifted 5 units to the right and 3 units down to match the corresponding points of the triangle in quadrant 1.