Determine if AABC is acute, obtuse, or right. A(1,5), B(-3,-3), C(1,-5) Acute triangle Obtuse triangle Right triangle This triangle is impossible
Determine if AABC is acute, obtuse, or right. A(1,5), B(-3,-3), C(1,-5) Acute triangle Obtuse triangle Right triangle This triangle is impossible
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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Question
Is it acute
Obtuse or right triangle ?
Justify the answer in numbers please.
![## Determining the Nature of Triangle \( \triangle ABC \)
### Problem Statement:
Determine if \( \triangle ABC \) is acute, obtuse, or right.
The coordinates of the points are:
- \( A(1, 5) \)
- \( B(-3, -3) \)
- \( C(1, -5) \)
### Options:
1. \( \bigcirc \) Acute triangle
2. \( \bigcirc \) Obtuse triangle
3. \( \bigcirc \) Right triangle (Selected)
4. \( \bigcirc \) This triangle is impossible
### Question:
Justify your answer with an equation or inequality:
\[ \text{Input Field:} \ [\textit{justify in numbers}] \ \] [This field allows you to enter your mathematical justification.]
### Graphical Representation:
On the right side of the page, there is a graph with a coordinate system ranging from \(-8\) to \(8\) on both axes. The points are marked and color-coded as follows:
- Point \( A(1, 5) \) is marked with a red dot.
- Point \( B(-3, -3) \) is marked with a green dot.
- Point \( C(1, -5) \) is marked with a blue dot.
### Hint:
*Move points around to help you.* This indicates that you can interact with the points on the graph to further understand their positions and the type of triangle they form.
### Instructions:
To determine the type of triangle \( \triangle ABC \):
1. Calculate the lengths of the sides using the distance formula.
2. Use the Pythagorean theorem to check if the triangle is right-angled.
3. Justify your conclusion with appropriate calculations and equations.
### Explanation:
To verify if \( \triangle ABC \) is a right triangle, calculate the distances between each pair of points to find the lengths of the sides. Then, use the Pythagorean theorem to check if the sum of the squares of the two shorter sides equals the square of the longest side.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F305a5581-2656-4b34-9e14-4b41bb9e3ef9%2F7d256180-e46a-453e-a9d8-e661d05053b0%2Fw70mzh4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Determining the Nature of Triangle \( \triangle ABC \)
### Problem Statement:
Determine if \( \triangle ABC \) is acute, obtuse, or right.
The coordinates of the points are:
- \( A(1, 5) \)
- \( B(-3, -3) \)
- \( C(1, -5) \)
### Options:
1. \( \bigcirc \) Acute triangle
2. \( \bigcirc \) Obtuse triangle
3. \( \bigcirc \) Right triangle (Selected)
4. \( \bigcirc \) This triangle is impossible
### Question:
Justify your answer with an equation or inequality:
\[ \text{Input Field:} \ [\textit{justify in numbers}] \ \] [This field allows you to enter your mathematical justification.]
### Graphical Representation:
On the right side of the page, there is a graph with a coordinate system ranging from \(-8\) to \(8\) on both axes. The points are marked and color-coded as follows:
- Point \( A(1, 5) \) is marked with a red dot.
- Point \( B(-3, -3) \) is marked with a green dot.
- Point \( C(1, -5) \) is marked with a blue dot.
### Hint:
*Move points around to help you.* This indicates that you can interact with the points on the graph to further understand their positions and the type of triangle they form.
### Instructions:
To determine the type of triangle \( \triangle ABC \):
1. Calculate the lengths of the sides using the distance formula.
2. Use the Pythagorean theorem to check if the triangle is right-angled.
3. Justify your conclusion with appropriate calculations and equations.
### Explanation:
To verify if \( \triangle ABC \) is a right triangle, calculate the distances between each pair of points to find the lengths of the sides. Then, use the Pythagorean theorem to check if the sum of the squares of the two shorter sides equals the square of the longest side.
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