O Triangle ABC is shown in the xy-coordinate plane. c- 5-4-3-2-1 2345 The triangle will be rotated 180° clockwise around the point (3, 4) to create AA'B'C'. Which Ocharacteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select all that apply. A. the coordinates of A' B. the coordinates of B C. the perimeter of AA'B'C' D. the area of AA'B'C' E. the measure of B F. the length of segment A'B mil
O Triangle ABC is shown in the xy-coordinate plane. c- 5-4-3-2-1 2345 The triangle will be rotated 180° clockwise around the point (3, 4) to create AA'B'C'. Which Ocharacteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select all that apply. A. the coordinates of A' B. the coordinates of B C. the perimeter of AA'B'C' D. the area of AA'B'C' E. the measure of B F. the length of segment A'B mil
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![### Geometry: Rotating Triangles in the Coordinate Plane
**Triangle Rotation Example**
#### Triangle \(ABC\) in the Coordinate Plane
Here, we have a right triangle \(ABC\) displayed on a standard \(xy\)-coordinate plane.
- **Triangle's Vertices:**
- Point \(A\) is located at \((-3,1)\)
- Point \(B\) is at \((0,4)\)
- Point \(C\) is at \((3,1)\)
[Graph Description]
- The triangle \(ABC\) is illustrated on the grid.
- \(A\), \(B\), and \(C\) are connected to form triangle \(ABC\).
The triangle will be rotated 180° clockwise around the point \((3,4)\) to create triangle \(A'B'C'\). In this transformation, you need to identify which characteristics will remain the same in both triangles \(A'B'C'\) and \(ABC\).
#### Question
Which characteristics of \(\triangle A'B'C'\) will be the same for the corresponding characteristics of \(\triangle ABC\)?
Select all that apply:
1. The coordinates of \(A'\)
2. The coordinates of \(B'\)
3. The perimeter of \(\triangle A'B'C'\)
4. The area of \(\triangle A'B'C'\)
5. The measure of \(\angle B'\)
6. The length of segment \(A'B'\)
#### Answer Choices
- **A.** The coordinates of \(A'\)
- **B.** The coordinates of \(B'\)
- **C.** The perimeter of \(\triangle A'B'C'\)
- **D.** The area of \(\triangle A'B'C'\)
- **E.** The measure of \(\angle B'\)
- **F.** The length of segment \(A'B'\)
#### Additional Information
**Exterior Angles of Polygons**
Below the main question, there is an unrelated statement that reads:
"The degree measure of each exterior angle of a regular octagon ..."
---
This setup helps students understand the concepts of rotation in geometry, specifically focusing on how certain properties of geometric shapes are preserved under rotations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffac2e1b9-633f-466d-8122-66a15402491c%2Fbb19b1a8-9328-4293-b483-53ac570ac4b5%2F685b3ls_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry: Rotating Triangles in the Coordinate Plane
**Triangle Rotation Example**
#### Triangle \(ABC\) in the Coordinate Plane
Here, we have a right triangle \(ABC\) displayed on a standard \(xy\)-coordinate plane.
- **Triangle's Vertices:**
- Point \(A\) is located at \((-3,1)\)
- Point \(B\) is at \((0,4)\)
- Point \(C\) is at \((3,1)\)
[Graph Description]
- The triangle \(ABC\) is illustrated on the grid.
- \(A\), \(B\), and \(C\) are connected to form triangle \(ABC\).
The triangle will be rotated 180° clockwise around the point \((3,4)\) to create triangle \(A'B'C'\). In this transformation, you need to identify which characteristics will remain the same in both triangles \(A'B'C'\) and \(ABC\).
#### Question
Which characteristics of \(\triangle A'B'C'\) will be the same for the corresponding characteristics of \(\triangle ABC\)?
Select all that apply:
1. The coordinates of \(A'\)
2. The coordinates of \(B'\)
3. The perimeter of \(\triangle A'B'C'\)
4. The area of \(\triangle A'B'C'\)
5. The measure of \(\angle B'\)
6. The length of segment \(A'B'\)
#### Answer Choices
- **A.** The coordinates of \(A'\)
- **B.** The coordinates of \(B'\)
- **C.** The perimeter of \(\triangle A'B'C'\)
- **D.** The area of \(\triangle A'B'C'\)
- **E.** The measure of \(\angle B'\)
- **F.** The length of segment \(A'B'\)
#### Additional Information
**Exterior Angles of Polygons**
Below the main question, there is an unrelated statement that reads:
"The degree measure of each exterior angle of a regular octagon ..."
---
This setup helps students understand the concepts of rotation in geometry, specifically focusing on how certain properties of geometric shapes are preserved under rotations.
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