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Determine whether poss. to have triangle w/ given vertices
- Thread starter rubyred
- Start date
Re: Detrmine traingle verticies help asap!
Simply plot the three points on a graph and connect the points. You get a triangle.
In general, any three points that are not colinear (on the same line) define a plane -- and a triangle.
To demonstrate algebraically that the points are not colinear, simply calculate the slopes between all the points. If they are all different, then they are not on the same line.
1. Determine whether it is possible to have atraingle with vertices A(1, -1), B(7,7) C(2,-5) Write Yes or No and Explain your answer.
Simply plot the three points on a graph and connect the points. You get a triangle.
In general, any three points that are not colinear (on the same line) define a plane -- and a triangle.
To demonstrate algebraically that the points are not colinear, simply calculate the slopes between all the points. If they are all different, then they are not on the same line.
Re: Detrmine traingle verticies help asap!
Hello, rubyred!
Three points always determine a triangle ... unless the points are collinear.
\(\displaystyle \text{Examine the slopes: }\:\begin{array}{ccccccc}m_{_{AB}} &=& \frac{7-(\text{-}1)}{7-1} &=& \frac{4}{3} \\ \\[-3mm] m_{_{AC}} &=& \frac{-5-(\text{-}1)}{2-1} &=& -4 \end{array}\qquad\text{The points are }not\text{ collinear.}\)
. . \(\displaystyle \text{Therefore, points }A,B,C\text{ form a triangle.}\)
Hello, rubyred!
1. Determine whether it is possible to have a triangle with vertices A(1,-1), B(7,7) C(2,-5).
Write Yes or No and Explain your answer.
Three points always determine a triangle ... unless the points are collinear.
\(\displaystyle \text{Examine the slopes: }\:\begin{array}{ccccccc}m_{_{AB}} &=& \frac{7-(\text{-}1)}{7-1} &=& \frac{4}{3} \\ \\[-3mm] m_{_{AC}} &=& \frac{-5-(\text{-}1)}{2-1} &=& -4 \end{array}\qquad\text{The points are }not\text{ collinear.}\)
. . \(\displaystyle \text{Therefore, points }A,B,C\text{ form a triangle.}\)