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.Describe 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 translation, then transformation translation, then transformation rotation, then translation rotation, then translation translation, then reflection translation, then reflection reflection, then translation

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To show that the triangle in Quadrant IV is congruent to the triangle in Quadrant II, we can describe the sequence of transformations necessary to map the former onto the latter.

Reflection: First, we reflect the triangle in Quadrant IV across the y-axis. This transformation will move the triangle from the fourth quadrant to the second quadrant.

Translation: After the reflection, the triangle will need to be translated (moved) to align perfectly with the triangle in Quadrant II.

Thus, the correct response for the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II is reflection, then translation.

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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.Describe 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 translation, then transformation translation, then transformation rotation, then translation rotation, then translation translation, then reflection translation, then reflection reflection, then translation

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To show that the triangle in Quadrant IV is congruent to the triangle in Quadrant II, we can describe the sequence of transformations necessary to map the former onto the latter.

Reflection: First, we reflect the triangle in Quadrant IV across the y-axis. This transformation will move the triangle from the fourth quadrant to the second quadrant.
Translation: After the reflection, the triangle will need to be translated (moved) to align perfectly with the triangle in Quadrant II.

Thus, the correct response for the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II is reflection, then translation.

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GPT-4o mini · Answer

To show that the triangle in Quadrant IV is congruent to the triangle in Quadrant II, we can describe the sequence of transformations necessary to map the former onto the latter.

Reflection: First, we reflect the triangle in Quadrant IV across the y-axis. This transformation will move the triangle from the fourth quadrant to the second quadrant.
Translation: After the reflection, the triangle will need to be translated (moved) to align perfectly with the triangle in Quadrant II.

Thus, the correct response for the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II is reflection, then translation.