Use the image to answer the question.

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 3 right parenthesis, upper B left parenthesis 1 comma negative 1 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 2 right parenthesis, and upper H left parenthesis negative 4 comma 2 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.

△ABC is congruent to △GHE . Describe a sequence of transformations from △ABC to △GHE that proves their congruence.

(2 points)

4 to 5 sentences please

Answer 1

To prove that △ABC is congruent to △GHE, we can use a sequence of transformations. First, we can translate △ABC 4 units to the left to align point A at (-1, -3) with point G at (-2, 2). This translation is denoted as a -4 unit horizontal shift. Next, we can reflect △ABC across the x-axis to flip it upside down, keeping point A at (-1, -3) and now aligning point B at (1, -1) with point H at (-4, 2). This reflection is denoted as a reflection across the x-axis. Finally, we can reflect the entire triangle across the y-axis to obtain △GHE, aligning point C at (4, -3) with point E at (-2, 5). This reflection is denoted as a reflection across the y-axis. These three transformations, a translation, a reflection across the x-axis, and a reflection across the y-axis, prove the congruence of △ABC and △GHE.