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 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)
To prove that triangles ABC and GHE are congruent, we can use a sequence of transformations.
1. Translation: Start by translating triangle ABC from point A(1, -3) to point E(-2, 5). This can be done by moving the entire triangle 3 units horizontally to the left and 8 units vertically upwards.
2. Reflection: Reflect triangle ABC across the x-axis. This will change the orientation of the triangle and its vertices. After reflection, the image of triangle ABC will be congruent to triangle GHE.
Therefore, the sequence of transformations from triangle ABC to triangle GHE is a translation followed by a reflection across the x-axis.