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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 reflection
translation, then reflection

translation, then transformation
translation, then transformation

reflection, then translation

1 answer

To move the triangle in Quadrant IV to the triangle in Quadrant II and show that the triangles are congruent, the correct sequence of steps would be:

reflection, then translation

Here's why:

  1. Reflection: The triangle in Quadrant IV needs to be reflected across the y-axis to move it to Quadrant II. This changes the x-coordinates of the vertices from positive to negative while keeping the y-coordinates the same.

  2. Translation: After reflecting the triangle, it may require a translation (shift up) to align it with the position of the triangle in Quadrant II.

Thus, the final answer is reflection, then translation.