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use the image described 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 negative 6 comma negative 2 right parenthesis, upper B left parenthesis negative 4 comma negative 5 right parenthesis, and upper C left parenthesis negative 1 comma negative 5 right parenthesis. The triangle upper E upper G upper H has its vertices marked with closed points at upper E left parenthesis 4 comma 6 right parenthesis, upper G left parenthesis 7 comma 6 right parenthesis, and upper H left parenthesis 2 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 transformations needed to move triangle ABC to triangle EGH to show that the triangles are congruent?

reflection over the x-axis, then a translation of (__)

2 answers

To move triangle ABC to triangle EGH and show that the triangles are congruent, we can follow these steps:

  1. Reflection over the x-axis:

    • Reflect triangle ABC across the x-axis. This will transform the vertices of triangle ABC from their original positions:
      • A(-6, -2) → A'(-6, 2)
      • B(-4, -5) → B'(-4, 5)
      • C(-1, -5) → C'(-1, 5)

  2. Translation:

    • After reflecting triangle ABC, we need to translate the new triangle A'B'C' to match triangle EGH. The vertices of triangle EGH are:

      • E(4, 6)
      • G(7, 6)
      • H(2, 3)

    • The reflected and translated positions should ideally match the positions of triangle EGH.

    • We can find the translation by determining the difference between corresponding points. Taking the point A'(-6, 2) and wanting it to go to E(4, 6):

      • To move from -6 to 4 on the x-axis: \( 4 - (-6) = 10 \)
      • To move from 2 to 6 on the y-axis: \( 6 - 2 = 4 \)

    • Thus, the translation needed is (10, 4).

Putting this together, the sequence of transformations needed to move triangle ABC to triangle EGH is: Reflection over the x-axis, then a translation of (10, 4).

thats not right