Use 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. 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
rotation, then translation
rotation, then translation
translation, then transformation
The correct sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II and show that the triangles are congruent is:
1. Translation: Move the triangle in Quadrant IV to the corresponding position in Quadrant II without changing the orientation. The triangle's vertices would be moved from coordinates (1, -3), (1, -7), and (3, -3) to (-1, 3), (-1, 7), and (-3, 3) respectively.
2. Reflection: Reflect the translated triangle over the y-axis to match the orientation of the triangle in Quadrant II. The triangle's vertices would remain the same but the x-coordinates would change their signs. The new vertices would be (-1, 3), (-1, 7), and (-3, 3).
Therefore, the correct answer is "translation, then reflection".