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 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)
(
,
)
Remaining Attempts : 3

Answer 1

To determine the sequence of transformations needed to move triangle ABC to triangle EGH and show that the triangles are congruent, we will analyze the positions of the triangles on the coordinate plane.

1. **Identify the vertices of triangle ABC:**
- A(-6, -2)
- B(-4, -5)
- C(-1, -5)

2. **Identify the vertices of triangle EGH:**
- E(4, 6)
- G(7, 6)
- H(2, 3)

### Steps to Transform:

**Step 1: Translation**
- The first transformation needed is a translation. We can translate triangle ABC to triangle EGH by moving it up and to the right.

- The translation can be defined as:
- Move right by 10 units (from -6 to 4, for point A).
- Move up by 8 units (from -2 to 6, for point A).

So, the translation vector can be (10, 8).

**Step 2: Rotation**
- Once translated, it may also be necessary to rotate triangle ABC to match the orientation of triangle EGH. The exact amount of rotation will depend on the specific angles of the triangles, so if needed, determine the angle of rotation that aligns the triangles properly.

### Sequence of Transformations:
1. **Translation:** move right by 10 units and up by 8 units.
2. **Rotation:** rotate about an appropriate point, most likely the centroid of triangle ABC after translation, to align the sides of the triangles.

Thus, the answer to the sequence of transformations is:

**(Translation by (10, 8), followed by a possible rotation)**

Please adjust the rotation step based on the actual orientation needed after translating triangle ABC using the provided coordinates.