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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?

(1 point)
reflection over the x
-axis, then a translation of (
)
Remaining Attempts : 3
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Answer 1

To determine the sequence of transformations needed to move triangle ABC to triangle EGH, we first analyze their positions on the coordinate plane.

Triangle ABC:

• A(-6, -2)
• B(-4, -5)
• C(-1, -5)

Triangle EGH:

• E(4, 6)
• G(7, 6)
• H(2, 3)

Step 1: Reflection

The first transformation is a reflection over the x-axis. This transformation changes the y-coordinates of triangle ABC from negative to positive:

• A(-6, -2) → A'(-6, 2)
• B(-4, -5) → B'(-4, 5)
• C(-1, -5) → C'(-1, 5)

Step 2: Translation

Next, we observe that the reflected triangle A'B'C' still does not match triangle EGH. We will translate the reflected points to match EGH.

To determine the translation vector, we can find the distance needed to move point A' to E:

From A'(-6, 2) to E(4, 6):

• The change in x = 4 - (-6) = 10
• The change in y = 6 - 2 = 4

Thus, we translate triangle A'B'C' by the vector (10, 4).

Summary of Transformations

1. Reflect triangle ABC over the x-axis.
2. Translate the resulting triangle by (10, 4).

Thus, the complete transformation is: Reflection over the x-axis, then a translation of (10, 4).