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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

reflection, then translation
reflection, then translation

translation, then transformation
translation, then transformation

translation, then reflection
translation, then reflection

rotation, then translation

Answer 1

To show that the triangles in Quadrant IV and Quadrant II are congruent, we can describe the steps as follows:

1. Reflection: First, reflect the triangle in Quadrant IV across the y-axis. This will move the triangle from Quadrant IV to Quadrant II, aligning it with the triangle that is already in Quadrant II.

2. Translation: Next, translate the reflected triangle to exactly match the vertices of the triangle in Quadrant II.

Therefore, the correct sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II is:

reflection, then translation.