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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. Two triangles, upper A upper B upper C and upper E upper G upper H, are plotted on the graph. The triangle upper A upper B upper C has its vertices marked with closed points at upper A left parenthesis 1 comma negative 1 right parenthesis, upper B left parenthesis 1 comma negative 3 right parenthesis, and upper C left parenthesis 4 comma negative 3 right parenthesis. The triangle upper E upper G upper H has its vertices marked with closed points at upper E left parenthesis negative 2 comma 5 right parenthesis, upper G left parenthesis negative 2 comma 3 right parenthesis, and upper H left parenthesis negative 5 comma 3 right parenthesis. In triangle upper E upper G upper H, side upper E upper G is labeled as h, side upper G upper H is labeled as e, and side upper H upper E is labeled as g.

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

rotation 90 degrees clockwise, then a translation of (1, 6)

reflection to Quadrant III, then a translation of (−1, 6)

translation to Quadrant II, then a rotation 90 degrees counterclockwise

reflection to Quadrant I, then a translation of (3, 2)

1 answer

To move triangle ABC in Quadrant IV to triangle EGH in Quadrant II and show that they are congruent, you can follow these steps:

  1. Reflection to Quadrant II: First, you can reflect triangle ABC over the y-axis, which will move it from Quadrant IV to Quadrant II.

  2. Translation: After reflecting, you would need to translate the reflected triangle E'F'G' (the reflected version of triangle ABC) to align it with triangle EGH. The translation would be (−1, 6).

Therefore, the correct sequence of steps would be: reflection to Quadrant III, then a translation of (−1, 6).

This means the correct option would be the second choice: reflection to Quadrant III, then a translation of (−1, 6).

(Note: It seems there was an inconsistency in using Quadrant II and Quadrant III in the reflection description; ensuring the accurate placement post-reflection is important).