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
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd1bb1f9-fb23-4384-980b-2faa98f7c41c%2F4a221d2c-d0d9-411b-8256-ad5e01cbe5ca%2Fnkmzvsf_processed.jpeg&w=3840&q=75)
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