Use the image to answer the question.

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. 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

rotation, then translation
rotation, then translation

translation, then transformation
translation, then transformation

reflection, then translation
reflection, then translation

translation, then reflection

Answer 1

To describe the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II, we can analyze the positions of the triangles.

1. The triangle in Quadrant IV has vertices at (1, -3), (1, -7), and (3, -3).
2. The triangle in Quadrant II has vertices at (-1, 3), (-5, 3), and (-5, 5).

To move the triangle from Quadrant IV to Quadrant II:

• First, we can reflect the triangle across the x-axis. This will move the points from negative y-coordinates to positive y-coordinates while keeping their x-coordinates the same (ignoring the sign).
• Then, we need to translate the triangle leftwards to align it with the triangle in Quadrant II.

Thus, the sequence of steps to show that the triangles are congruent is:

reflection, then translation