Use the image to answer the question.

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 (
)
Remaining Attempts : 3

Answer 1

To determine the transformations that demonstrate that the triangles in question are congruent, you need to compare their positions and orientations on the coordinate plane.

1. Rotation: The triangle in quadrant 2 appears to be rotated to align with the triangle in quadrant 1. The exact degree of rotation can be found by checking the coordinates, but since we don't have the image, you can visually estimate the rotation angle based on the orientation of the triangles.

2. Translation: After rotation, the triangle may need to be translated (shifted) horizontally and/or vertically to perfectly overlay on the triangle in quadrant 1. The direction and magnitude of the translation can also be visually assessed based on the plotted points.

Let's summarize the transformations:

• Rotation: Estimate the degree of rotation, often it can be a standard angle like 90, 180, etc.
• Translation: You'll need to specify the horizontal and vertical shift. You can express this as (x, y) indicating how far the triangle is shifted along the x-axis and y-axis.

Answer:

Rotation of 90 degrees counterclockwise and translation of (1, 0)