Finding the unknown points of a second triangle

In summary, the purpose of finding the unknown points of a second triangle is to determine the exact location and dimensions of the triangle in relation to the first triangle. The most common methods used for this are trigonometric ratios, the Pythagorean theorem, and the law of cosines. To find the unknown points, at least three measurements or angles of both triangles are needed. This concept has real-life applications in fields such as construction, navigation, and surveying. However, there are limitations to this method, including assuming the triangles are on a two-dimensional plane and relying on the accuracy of measurements.
  • #1
Will15
5
0

Homework Statement


Triangle A has three points a(2,3)b(0,0)c(2,0) and its center is (2/3,1). Find the other three points of Triangle B with a center of (4/3,3).


Homework Equations


Center of a triangle:
x = ax+bx+cx /3
y = ay+by+cy / 3

Magnitude = <a,b> , √(a^2+b^2)

The Attempt at a Solution


1)Obtaining the vector of AB by subtracting the two center <4/3-2/3, 3-1> = <2/3,2>
2)Magnitude of vector AB is (2*√10)/3
3)Adding the magnitude to the three points of triangle A
4)Check answer by calculating the center with the 3 new points, should match with the given center above.

Step 4 is where I'm stuck, I can't get the same x center.
 
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  • #2
Will15 said:

Homework Statement


Triangle A has three points a(2,3)b(0,0)c(2,0) and its center is (2/3,1). Find the other three points of Triangle B with a center of (4/3,3).


Homework Equations


Center of a triangle:
x = ax+bx+cx /3
y = ay+by+cy / 3

Magnitude = <a,b> , √(a^2+b^2)

The Attempt at a Solution


1)Obtaining the vector of AB by subtracting the two center <4/3-2/3, 3-1> = <2/3,2>
2)Magnitude of vector AB is (2*√10)/3
3)Adding the magnitude to the three points of triangle A
4)Check answer by calculating the center with the 3 new points, should match with the given center above.

Step 4 is where I'm stuck, I can't get the same x center.

How is triangle B related to triangle A?
 
  • #3
Mark44 said:
How is triangle B related to triangle A?

The relation is unknown.
 

FAQ: Finding the unknown points of a second triangle

What is the purpose of finding the unknown points of a second triangle?

The purpose of finding the unknown points of a second triangle is to determine the exact location and dimensions of the triangle in relation to the first triangle. This information can be used in various fields such as geometry, engineering, and physics.

What are the methods used to find the unknown points of a second triangle?

The most common methods used to find the unknown points of a second triangle are using trigonometric ratios, the Pythagorean theorem, and the law of cosines. These methods involve using known measurements and relationships of the two triangles to solve for the unknown points.

What information is needed to find the unknown points of a second triangle?

To find the unknown points of a second triangle, you will need to know at least three measurements or angles of both triangles. These can include side lengths, angles, or a combination of both. The more information you have, the easier it will be to solve for the unknown points.

What are some real-life applications of finding the unknown points of a second triangle?

Finding the unknown points of a second triangle can be applied in various fields such as construction, navigation, and surveying. For example, engineers may use this concept to determine the dimensions and positioning of structures, while pilots may use it to navigate their aircraft using triangulation.

Are there any limitations to finding the unknown points of a second triangle?

Yes, there are some limitations to finding the unknown points of a second triangle. This method assumes that the two triangles are in a two-dimensional plane and do not account for any potential errors or discrepancies in the measurements. It also relies on the accuracy of the provided measurements, which may not always be exact.

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