Triangle #2 Triangle RST has coordinates R(-1,7), S(3,-1), and T(9,2). 12 Find the length of ST. O 37 O 45 V143 /145 13 Find the length of RT. O 4 89 125 O V145 14 Classify the triangle O Scalene Triangle Isosceles Triangle Equilateral Triangle Scalene Right Triangle Isosceles Right Triangle

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
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Classify the triangle
### Triangle #2 Coordinates and Classification

This section helps understand the properties of Triangle RST with given coordinates of R, S, and T. Below are three important questions to help deduce its lengths and type:

#### 1. Triangle #2 Description
- **Coordinates**:
  - Point \( R = (1, 7) \)
  - Point \( S = (3, -1) \)
  - Point \( T = (9, 2) \)

#### 2. Questions and Solutions

##### Question 12: Find the length of ST.
- **Choices**:
  - \( \sqrt{143} \)
  - \( \sqrt{45} \)
  - \( \sqrt{37} \)
  - \( \sqrt{145} \)

##### Question 13: Find the length of RT.
- **Choices**:
  - 4
  - \( \sqrt{89} \)
  - \( \sqrt{125} \)
  - \( \sqrt{145} \)

##### Question 14: Classify the triangle.
- **Choices**:
  - Scalene Triangle
  - Isosceles Triangle
  - Equilateral Triangle
  - Scalene Right Triangle
  - Isosceles Right Triangle

#### Practical Application:
To solve for the lengths and classification:
- **Use the distance formula**: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

By calculating the distances between each pair of points, one can determine the side lengths of the triangle. Further, comparing these lengths allows one to classify the triangle accordingly. 

This exploration enhances understanding of geometric properties and the application of algebraic formulas in coordinate geometry.

### Graphs and Diagrams:
In this case, there are no graphs or diagrams provided. However, drawing the triangle on a coordinate plane can help visualize the points and confirm the calculated distances.
Transcribed Image Text:### Triangle #2 Coordinates and Classification This section helps understand the properties of Triangle RST with given coordinates of R, S, and T. Below are three important questions to help deduce its lengths and type: #### 1. Triangle #2 Description - **Coordinates**: - Point \( R = (1, 7) \) - Point \( S = (3, -1) \) - Point \( T = (9, 2) \) #### 2. Questions and Solutions ##### Question 12: Find the length of ST. - **Choices**: - \( \sqrt{143} \) - \( \sqrt{45} \) - \( \sqrt{37} \) - \( \sqrt{145} \) ##### Question 13: Find the length of RT. - **Choices**: - 4 - \( \sqrt{89} \) - \( \sqrt{125} \) - \( \sqrt{145} \) ##### Question 14: Classify the triangle. - **Choices**: - Scalene Triangle - Isosceles Triangle - Equilateral Triangle - Scalene Right Triangle - Isosceles Right Triangle #### Practical Application: To solve for the lengths and classification: - **Use the distance formula**: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] By calculating the distances between each pair of points, one can determine the side lengths of the triangle. Further, comparing these lengths allows one to classify the triangle accordingly. This exploration enhances understanding of geometric properties and the application of algebraic formulas in coordinate geometry. ### Graphs and Diagrams: In this case, there are no graphs or diagrams provided. However, drawing the triangle on a coordinate plane can help visualize the points and confirm the calculated distances.
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