Question

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. 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 translation to Quadrant II, then a rotation 90 degrees counterclockwise translation to Quadrant II, then a rotation 90 degrees counterclockwise reflection to Quadrant III, then a translation of (−1, 6) ( − 1 , 6 ) reflection to Quadrant III, then a translation of left parenthesis negative 1 comma 6 right parenthesis reflection to Quadrant I, then a translation of (3, 2) ( 3 , 2 ) reflection to Quadrant I, then a translation of left parenthesis 3 comma 2 right parenthesis rotation 90 degrees clockwise, then a translation of (1, 6)

Answer 1

To determine the correct sequence of steps to move triangle EGH (in Quadrant II) to triangle ABC (in Quadrant IV) and show that they are congruent, we can analyze the coordinates and movements required.

1. **Identify the location of triangles**:
- Triangle ABC is in Quadrant IV with vertices A(1, -1), B(1, -3), and C(4, -3).
- Triangle EGH is in Quadrant II with vertices E(-2, 5), G(-2, 3), and H(-5, 3).

2. **Identify transformations**:
- A common way to move triangles involves translations, rotations, or reflections.

3. **Choose the correct movements**:
- **Reflection to Quadrant III**: Triangle EGH can be reflected across the y-axis to begin moving it toward Quadrant IV. This will place E at (2, 5), G at (2, 3), and H at (5, 3), which now places it closer to Quadrant IV.
- **Translation of (-1, 6)**: This would finalize the movement of EGH into the correct coordinates in Quadrant IV to match the vertices of triangle ABC.

Thus, the correct sequence of transformations is:

**Reflection to Quadrant III, then a translation of (-1, 6)**.

So the final answer would be:

**Reflection to Quadrant III, then a translation of (-1, 6)**.