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 translation, then transformation translation, then transformation translation, then reflection translation, then reflection reflection, then translation reflection, then translation rotation, then translation

Answer 1

To determine the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II, we need to analyze the movements involved:

1. **Reflection**: The triangle in Quadrant IV has points with positive x-coordinates and negative y-coordinates. To move this triangle to Quadrant II, we can first reflect it over the y-axis. This will change the signs of the x-coordinates, moving points from Quadrant IV to Quadrant III.

2. **Translation**: The next step involves translating the reflected triangle from Quadrant III to Quadrant II. This involves moving the triangle to the left across the y-axis.

Given this analysis, the correct sequence of steps to show that the triangles are congruent is **reflection, then translation**.