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Question

An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. Three triangles are plotted on the graph. The triangle upper A upper B upper C has its vertices marked with closed points at upper A left parenthesis 2 comma negative 2 right parenthesis, upper B left parenthesis 2 comma negative 4 right parenthesis, and upper C left parenthesis 5 comma negative 4 right parenthesis. The second triangle, placed in the second quadrant, has its vertices marked with closed points at left parenthesis negative 3 comma 6 right parenthesis, left parenthesis negative 5 comma 6 right parenthesis, and left parenthesis negative 5 comma 3 right parenthesis. The third triangle, placed in the third quadrant, has its vertices marked with closed points at left parenthesis negative 2 comma negative 2 right parenthesis, left parenthesis negative 4 comma negative 2 right parenthesis, and left parenthesis negative 4 comma negative 5 right parenthesis. An arrow goes from the point left parenthesis negative 2 comma negative 2 right parenthesis to left parenthesis negative 3 comma 6 right parenthesis; an arrow goes from the point left parenthesis negative 4 comma negative 2 right parenthesis to left parenthesis negative 5 comma 6 right parenthesis; an arrow goes from left parenthesis negative 4 comma negative 5 right parenthesis to left parenthesis negative 5 comma 3 right parenthesis.

What sequence of transformations is depicted in the figure, proving the congruence of the triangles?

(1 point)
rotation of
degrees clockwise about the origin, then translation of (
)
Remaining Attempts : 3
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Answer 1

To determine the sequence of transformations that proves the congruence of the triangles described, we generally look for how the vertices of one triangle relate to those of another triangle.

1. Identifying the Triangles:

   • Triangle \( ABC \): Vertices \( A(2, -2) \), \( B(2, -4) \), \( C(5, -4) \).
   • Triangle in the second quadrant: Vertices \( (-3, 6) \), \( (-5, 6) \), \( (-5, 3) \).
   • Triangle in the third quadrant: Vertices \( (-2, -2) \), \( (-4, -2) \), \( (-4, -5) \).

2. Transformations:

   • The transformations involve an arrow from a point in the third quadrant going to a point in the second quadrant, and from one point in the third quadrant to another in the second quadrant.
   • Specifically, the arrows suggest a reflection or rotation that takes the triangle in the third quadrant to the triangle in the second quadrant.

3. Finding the Transformations:

   • Rotation: It looks like from the coordinates that the triangle is being rotated.
   • Degrees Clockwise: Determine the angle of rotation needed to move points from one quadrant to another. Examining the movement from the third quadrant to the second quadrant suggests a potential 90-degree counterclockwise (or 270 degrees clockwise) rotation.
   • Translation: After rotation, you'll need to translate the points to align them correctly with the coordinates of the new triangle.

Given these observations:

The sequence of transformations that proves the congruence of the triangles is likely a rotation of 90 degrees clockwise about the origin, then a translation (which adjusts the position to match the new coordinates).

Answer: Rotation of 90 degrees clockwise about the origin, then translation of (X, Y). (Exact values for translation need to be determined based on specific coordinates after rotation.)