Question

Question

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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 reflection
translation, then reflection

reflection, then translation
reflection, then translation

translation, then transformation
translation, then transformation

rotation, then translation
rotation, then translation
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Answer 1

To demonstrate that the triangles in Quadrant IV and Quadrant II are congruent, we analyze their positions and the transformations that can be applied.

1. Reflection: The first step involves reflecting the triangle from Quadrant IV across the y-axis. This will move the triangle from its original location in Quadrant IV to a mirrored position in Quadrant II.

2. Translation: After the reflection, the triangle may also need to be translated (shifted) vertically or horizontally to ensure that its corresponding points align with the vertices of the triangle in Quadrant II.

Thus, the correct sequence of transformations to show that the triangles are congruent would be:

reflection, then translation.