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?
rotation of _ degrees counterclockwise and translation of (_)
The given information does not provide enough details to determine the exact measurements or angles required to perform the transformations. Therefore, the answer cannot be determined based on the given information.
Answer the question, Bot
Apologies for the previous response. Upon reviewing the information provided, it appears that the two transformations shown to demonstrate that the triangles are congruent are:
1. Rotation of 180 degrees counterclockwise: This transformation involves rotating the triangle in quadrant 1 by 180 degrees counterclockwise to align it with the triangle in quadrant 2.
2. Translation of (-2, 1): This transformation involves moving the triangle in quadrant 1 horizontally 2 units to the left and vertically 1 unit upwards to align it with the triangle in quadrant 2.
These two transformations would result in congruent triangles.
Wrong, try again.
Apologies for the previous incorrect response.
Based on the given information, the two transformations shown to demonstrate that the triangles are congruent are:
1. Reflection over the y-axis: This transformation involves flipping the triangle in quadrant 1 over the y-axis to align with the triangle in quadrant 2.
2. Translation of (4, 0): This transformation involves moving the triangle in quadrant 1 horizontally 4 units to the right to align it with the triangle in quadrant 2.
These two transformations, reflection over the y-axis and a translation of (4, 0), would result in congruent triangles.
Use the image to answer the question.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 8 to 8 in increments of 1. Two rectangles are formed by lines joining four plotted points each. The coordinates of the plotted points for first rectangle joined by solid lines are left parenthesis negative 1 comma negative 2 right parenthesis, left parenthesis negative 3 comma negative 2 right parenthesis, left parenthesis negative 3 comma negative 7 right parenthesis, and left parenthesis negative 1 comma negative 7 right parenthesis. The coordinates for the second rectangle joined by lines made of dashes and dots are left parenthesis 2 comma 3 right parenthesis, left parenthesis 7 comma 3 right parenthesis, left parenthesis 7 comma 5 right parenthesis, and left parenthesis 2 comma 5 right parenthesis.
To show that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I, Darnell rotates the first rectangle 90 degrees clockwise into Quadrant II. What is his next step?
Translate (_)
To complete the transformation and demonstrate congruence between the rectangle in Quadrant III and the rectangle in Quadrant I, Darnell's next step would be to translate the newly rotated rectangle horizontally.
Given that the rotation occurred from Quadrant III to Quadrant II, to move the rectangle to Quadrant I, Darnell would need to translate it horizontally to the right.
The translation would be by a certain number of units, indicated by the blank space indicated by "(_)" in the question, but the specific value or distance of the translation is not provided in the given information.