Congruent Figures Quick Check5 of 5 5 of 5 ItemsA coordinate plane with 4 quadrants shows x and y axes ranging from negative 8 to 8 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 3 right parenthesis, left parenthesis 3 comma negative 3 right parenthesis, and left parenthesis 1 comma negative 7 right parenthesis. The coordinates for the triangle in quadrant 2 are as follows left parenthesis negative 5 comma 3 right parenthesis, left parenthesis negative 1 comma 3 right parenthesis, and left parenthesis negative 5 comma 5 right parenthesis. The side joining the vertices at left parenthesis negative 5 comma 3 right parenthesis and left parenthesis negative 5 comma 5 right parenthesis is labeled as e. The side joining the vertices at left parenthesis negative 5 comma 5 right parenthesis and left parenthesis negative 1 comma 3 right parenthesis is labeled as g. The side joining the vertices at left parenthesis negative 5 comma 3 right parenthesis and left parenthesis negative 1 comma 3 right parenthesis is labeled as h. The coordinates of the plotted points for the triangle in quadrant 1 are left parenthesis 3 comma 1 right parenthesis, left parenthesis 7 comma 1 right parenthesis, and left parenthesis 3 comma 3 right parenthesis. Three rays join the complementary vertices of the triangles in quadrants 1 and 2. A ray connects point left parenthesis 3 comma 1 right parenthesis and the point left parenthesis negative 5 comma 3 right parenthesis. A ray connects point left parenthesis 7 comma 1 right parenthesis and the point left parenthesis negative 1 comma 3 right parenthesis. A ray connects point left parenthesis 3 comma 3 right parenthesis and the point left parenthesis negative 5 comma 5 right parenthesis. The arrow heads are on the vertices of the triangle in quadrant 2.A coordinate plane with 4 quadrants shows x and y axes ranging from negative 6 to 6 in increments of 1. Three triangles are formed by joining three plotted points each. The coordinates of the plotted points for the first triangle upper A upper B upper C joined by solid lines are upper A is left parenthesis negative 4 comma 5 right parenthesis, upper B is left parenthesis negative 1 comma 3 right parenthesis, and upper C is left parenthesis negative 3 comma 1 right parenthesis. The coordinates for the second triangle upper A prime upper B prime upper C prime joined by dotted lines are as follows: upper A prime at left parenthesis 4 comma 5 right parenthesis, upper B prime at left parenthesis 1 comma 3 right parenthesis, and upper C prime at left parenthesis 3 comma 1 right parenthesis. The coordinates of the plotted points for the third triangle upper A double prime upper B double prime upper C double prime joined by lines made of dashes and dots are as follows: upper A double prime at left parenthesis 1 comma 0 right parenthesis, upper B double prime at left parenthesis negative 2 comma negative 2 right parenthesis, and upper C double prime at left parenthesis 0 comma negative 4 right parenthesis.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 first triangle is placed in the first quadrant with vertices marked as closed points at the following coordinates: left parenthesis 3 comma 1 right parenthesis, left parenthesis 3 comma 3 right parenthesis, and left parenthesis 7 comma 1 right parenthesis. The second triangle is placed in the second quadrant with vertices marked as closed points at the following coordinates: left parenthesis negative 1 comma 3 right parenthesis, left parenthesis negative 5 comma 3 right parenthesis, and left parenthesis negative 5 comma 5 right parenthesis. The third triangle is placed in the fourth quadrant with vertices marked as closed points at the following coordinates: left parenthesis 1 comma negative 3 right parenthesis, left parenthesis 1 comma negative 7 right parenthesis, and left parenthesis 3 comma negative 3 right parenthesis. An arrow goes from the point left parenthesis 3 comma 1 right parenthesis to left parenthesis negative 5 comma 3 right parenthesis; an arrow goes from the point left parenthesis 3 comma 3 right parenthesis to left parenthesis negative 5 comma 5 right parenthesis; an arrow goes from left parenthesis 7 comma 1 right parenthesis to left parenthesis negative 1 comma 3 right parenthesis.An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. Three triangles are plotted on the graph. The first triangle is placed in the first quadrant with vertices marked as closed points at the following coordinates: left parenthesis 1 comma 1 right parenthesis, left parenthesis 3 comma 1 right parenthesis, and left parenthesis 2 comma 3 right parenthesis. The second triangle is placed in the second quadrant with vertices marked as closed points at the following coordinates: left parenthesis negative 2 comma 2 right parenthesis, left parenthesis negative 3 comma 4 right parenthesis, and left parenthesis negative 4 comma 2 right parenthesis. The third triangle is placed in the fourth quadrant with vertices marked as closed points at the following coordinates: 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. An arrow goes from the point left parenthesis 1 comma 1 right parenthesis to left parenthesis negative 4 comma 2 right parenthesis; an arrow goes from the point left parenthesis 2 comma 3 right parenthesis to left parenthesis negative 3 comma 4 right parenthesis; an arrow goes from left parenthesis 3 comma 1 right parenthesis to left parenthesis negative 2 comma 2 right parenthesis.QuestionUse the image to answer the 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. Two triangles, upper A upper B upper C and upper E upper G upper H, 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 1 comma negative 1 right parenthesis, upper B left parenthesis 1 comma negative 3 right parenthesis, and upper C left parenthesis 4 comma negative 3 right parenthesis. The triangle upper E upper G upper H has its vertices marked with closed points at upper E left parenthesis negative 2 comma 5 right parenthesis, upper G left parenthesis negative 2 comma 3 right parenthesis, and upper H left parenthesis negative 5 comma 3 right parenthesis. In triangle upper E upper G upper H, side upper E upper G is labeled as h, side upper G upper H is labeled as e, and side upper H upper E is labeled as g.What is the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent?(1 point)Responses reflection to Quadrant I, then a translation of (3, 2)reflection to Quadrant I, then a translation of left parenthesis 3 comma 2 right parenthesisrotation 90 degrees clockwise, then a translation of (1, 6)rotation 90 degrees clockwise, then a translation of left parenthesis 1 comma 6 right parenthesistranslation to Quadrant II, then a rotation 90 degrees counterclockwisetranslation to Quadrant II, then a rotation 90 degrees counterclockwisereflection to Quadrant III, then a translation of (−1, 6)

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To determine the sequence of steps to move the triangle in Quadrant IV to the triangle in Quadrant II and show that they are congruent, we can analyze the coordinates and their relative positions.

Reflect the triangle in Quadrant IV across the x-axis to move it into Quadrant III. This changes the coordinates of the triangle from:

\( (1, -1) \) to \( (1, 1) \)

\( (1, -3) \) to \( (1, 3) \)

\( (4, -3) \) to \( (4, 3) \)

Then, translate the triangle from Quadrant III to Quadrant II. The translation required would be moving left and up. Specifically, we would need to translate by \( (-5, 0) \):

\( (1, 1) \) translates to \( (-4, 1) \)

\( (1, 3) \) translates to \( (-4, 3) \)

\( (4, 3) \) translates to \( (-1, 3) \)

Therefore, the sequence of transformations involves a reflection then a translation.

Given the provided options for movement, the correct response would be "reflection to Quadrant I, then a translation of (3, 2)", noting that the incorrect designation of Quadrants is a bit confusing as one would first appear to be focusing on Quadrant III while moving towards II.

So, the best choice is reflection in Quadrant III, then a translation to Quadrant II. Their congruence is establishes through the transformations listed.

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Congruent Figures Quick Check5 of 5 5 of 5 ItemsA coordinate plane with 4 quadrants shows x and y axes ranging from negative 8 to 8 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 3 right parenthesis, left parenthesis 3 comma negative 3 right parenthesis, and left parenthesis 1 comma negative 7 right parenthesis. The coordinates for the triangle in quadrant 2 are as follows left parenthesis negative 5 comma 3 right parenthesis, left parenthesis negative 1 comma 3 right parenthesis, and left parenthesis negative 5 comma 5 right parenthesis. The side joining the vertices at left parenthesis negative 5 comma 3 right parenthesis and left parenthesis negative 5 comma 5 right parenthesis is labeled as e. The side joining the vertices at left parenthesis negative 5 comma 5 right parenthesis and left parenthesis negative 1 comma 3 right parenthesis is labeled as g. The side joining the vertices at left parenthesis negative 5 comma 3 right parenthesis and left parenthesis negative 1 comma 3 right parenthesis is labeled as h. The coordinates of the plotted points for the triangle in quadrant 1 are left parenthesis 3 comma 1 right parenthesis, left parenthesis 7 comma 1 right parenthesis, and left parenthesis 3 comma 3 right parenthesis. Three rays join the complementary vertices of the triangles in quadrants 1 and 2. A ray connects point left parenthesis 3 comma 1 right parenthesis and the point left parenthesis negative 5 comma 3 right parenthesis. A ray connects point left parenthesis 7 comma 1 right parenthesis and the point left parenthesis negative 1 comma 3 right parenthesis. A ray connects point left parenthesis 3 comma 3 right parenthesis and the point left parenthesis negative 5 comma 5 right parenthesis. The arrow heads are on the vertices of the triangle in quadrant 2.A coordinate plane with 4 quadrants shows x and y axes ranging from negative 6 to 6 in increments of 1. Three triangles are formed by joining three plotted points each. The coordinates of the plotted points for the first triangle upper A upper B upper C joined by solid lines are upper A is left parenthesis negative 4 comma 5 right parenthesis, upper B is left parenthesis negative 1 comma 3 right parenthesis, and upper C is left parenthesis negative 3 comma 1 right parenthesis. The coordinates for the second triangle upper A prime upper B prime upper C prime joined by dotted lines are as follows: upper A prime at left parenthesis 4 comma 5 right parenthesis, upper B prime at left parenthesis 1 comma 3 right parenthesis, and upper C prime at left parenthesis 3 comma 1 right parenthesis. The coordinates of the plotted points for the third triangle upper A double prime upper B double prime upper C double prime joined by lines made of dashes and dots are as follows: upper A double prime at left parenthesis 1 comma 0 right parenthesis, upper B double prime at left parenthesis negative 2 comma negative 2 right parenthesis, and upper C double prime at left parenthesis 0 comma negative 4 right parenthesis.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 first triangle is placed in the first quadrant with vertices marked as closed points at the following coordinates: left parenthesis 3 comma 1 right parenthesis, left parenthesis 3 comma 3 right parenthesis, and left parenthesis 7 comma 1 right parenthesis. The second triangle is placed in the second quadrant with vertices marked as closed points at the following coordinates: left parenthesis negative 1 comma 3 right parenthesis, left parenthesis negative 5 comma 3 right parenthesis, and left parenthesis negative 5 comma 5 right parenthesis. The third triangle is placed in the fourth quadrant with vertices marked as closed points at the following coordinates: left parenthesis 1 comma negative 3 right parenthesis, left parenthesis 1 comma negative 7 right parenthesis, and left parenthesis 3 comma negative 3 right parenthesis. An arrow goes from the point left parenthesis 3 comma 1 right parenthesis to left parenthesis negative 5 comma 3 right parenthesis; an arrow goes from the point left parenthesis 3 comma 3 right parenthesis to left parenthesis negative 5 comma 5 right parenthesis; an arrow goes from left parenthesis 7 comma 1 right parenthesis to left parenthesis negative 1 comma 3 right parenthesis.An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. Three triangles are plotted on the graph. The first triangle is placed in the first quadrant with vertices marked as closed points at the following coordinates: left parenthesis 1 comma 1 right parenthesis, left parenthesis 3 comma 1 right parenthesis, and left parenthesis 2 comma 3 right parenthesis. The second triangle is placed in the second quadrant with vertices marked as closed points at the following coordinates: left parenthesis negative 2 comma 2 right parenthesis, left parenthesis negative 3 comma 4 right parenthesis, and left parenthesis negative 4 comma 2 right parenthesis. The third triangle is placed in the fourth quadrant with vertices marked as closed points at the following coordinates: 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. An arrow goes from the point left parenthesis 1 comma 1 right parenthesis to left parenthesis negative 4 comma 2 right parenthesis; an arrow goes from the point left parenthesis 2 comma 3 right parenthesis to left parenthesis negative 3 comma 4 right parenthesis; an arrow goes from left parenthesis 3 comma 1 right parenthesis to left parenthesis negative 2 comma 2 right parenthesis.QuestionUse the image to answer the 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. Two triangles, upper A upper B upper C and upper E upper G upper H, 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 1 comma negative 1 right parenthesis, upper B left parenthesis 1 comma negative 3 right parenthesis, and upper C left parenthesis 4 comma negative 3 right parenthesis. The triangle upper E upper G upper H has its vertices marked with closed points at upper E left parenthesis negative 2 comma 5 right parenthesis, upper G left parenthesis negative 2 comma 3 right parenthesis, and upper H left parenthesis negative 5 comma 3 right parenthesis. In triangle upper E upper G upper H, side upper E upper G is labeled as h, side upper G upper H is labeled as e, and side upper H upper E is labeled as g.What is the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent?(1 point)Responses reflection to Quadrant I, then a translation of (3, 2)reflection to Quadrant I, then a translation of left parenthesis 3 comma 2 right parenthesisrotation 90 degrees clockwise, then a translation of (1, 6)rotation 90 degrees clockwise, then a translation of left parenthesis 1 comma 6 right parenthesistranslation to Quadrant II, then a rotation 90 degrees counterclockwisetranslation to Quadrant II, then a rotation 90 degrees counterclockwisereflection to Quadrant III, then a translation of (−1, 6)

1 answer

To determine the sequence of steps to move the triangle in Quadrant IV to the triangle in Quadrant II and show that they are congruent, we can analyze the coordinates and their relative positions.

Reflect the triangle in Quadrant IV across the x-axis to move it into Quadrant III. This changes the coordinates of the triangle from:
- \( (1, -1) \) to \( (1, 1) \)
- \( (1, -3) \) to \( (1, 3) \)
- \( (4, -3) \) to \( (4, 3) \)
Then, translate the triangle from Quadrant III to Quadrant II. The translation required would be moving left and up. Specifically, we would need to translate by \( (-5, 0) \):
- \( (1, 1) \) translates to \( (-4, 1) \)
- \( (1, 3) \) translates to \( (-4, 3) \)
- \( (4, 3) \) translates to \( (-1, 3) \)

Therefore, the sequence of transformations involves a reflection then a translation.

Given the provided options for movement, the correct response would be "reflection to Quadrant I, then a translation of (3, 2)", noting that the incorrect designation of Quadrants is a bit confusing as one would first appear to be focusing on Quadrant III while moving towards II.

So, the best choice is reflection in Quadrant III, then a translation to Quadrant II. Their congruence is establishes through the transformations listed.

Ask a New Question or answer this question.

GPT-4o mini · Answer

To determine the sequence of steps to move the triangle in Quadrant IV to the triangle in Quadrant II and show that they are congruent, we can analyze the coordinates and their relative positions.

Reflect the triangle in Quadrant IV across the x-axis to move it into Quadrant III. This changes the coordinates of the triangle from:
- \( (1, -1) \) to \( (1, 1) \)
- \( (1, -3) \) to \( (1, 3) \)
- \( (4, -3) \) to \( (4, 3) \)
Then, translate the triangle from Quadrant III to Quadrant II. The translation required would be moving left and up. Specifically, we would need to translate by \( (-5, 0) \):
- \( (1, 1) \) translates to \( (-4, 1) \)
- \( (1, 3) \) translates to \( (-4, 3) \)
- \( (4, 3) \) translates to \( (-1, 3) \)

Therefore, the sequence of transformations involves a reflection then a translation.

Given the provided options for movement, the correct response would be "reflection to Quadrant I, then a translation of (3, 2)", noting that the incorrect designation of Quadrants is a bit confusing as one would first appear to be focusing on Quadrant III while moving towards II.

So, the best choice is reflection in Quadrant III, then a translation to Quadrant II. Their congruence is establishes through the transformations listed.