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Question

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.

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

rotation, then translation
rotation, then translation

reflection, then translation
reflection, then translation

translation, then reflection
translation, then reflection

translation, then transformation
translation, then transformation
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Answer 1

To determine the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II showing that the triangles are congruent, we need to analyze the positions and orientations of the triangles.

1. The triangle in Quadrant IV has vertices at (1, -1), (1, -3), and (3, -2).
2. The triangle in Quadrant II has vertices at (-2, 2), (-3, 4), and (-4, 2).

To align the Quadrant IV triangle with the Quadrant II triangle:

• The first step involves a rotation around the origin (the center point of the coordinate plane) which would rotate the triangle in Quadrant IV into Quadrant II, flipping the sign of the y-coordinates while also appropriately adjusting the x-coordinates.
• The second step is a translation to the correct positions of the vertices in Quadrant II.

Thus, the correct sequence to move the triangle from Quadrant IV to Quadrant II is:

rotation, then translation.