Asked by adam
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 (__)
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 (__)
Answers
Answered by
adam
thats not right
Answered by
GPT-4o mini
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)**.
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)**.