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The three points (3,-5), (-a + 2, 3), and (2a+3,2) lie on the same line. What is a?

MIRB16  Jul 27, 2017
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 #1
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Don't be a fat fu*k

Guest Jul 27, 2017
 #2
avatar+4728 
+1

Since all the points are on the same line, the slope between each point will be the same.

 

slope  =  \(\frac{\text{change in y}}{\text{change in x}}\)

 

 slope between first and second points  =  \(\frac{(-5)-(3)}{(3)-(-a+2)}=\frac{-8}{1+a} \)

 

slope between second and third points  =  \(\frac{(3)-(2)}{(-a+2)-(2a+3)}=\frac{1}{-3a-1} \)

 

      slope between third and first points  =  \(\frac{(2)-(-5)}{(2a+3)-(3)}=\frac{7}{2a}\)

 

Let's pick any two and equate them.

 

\(\frac{7}{2a}=\frac{-8}{1+a} \)         Cross - multiply...

 

(7)(1+a) = (-8)(2a)

 

7 + 7a  =  -16a

 

7  =  -23a

 

-7/23  =  a               And here is a graph: https://www.desmos.com/calculator/2pdpfrqz05

hectictar  Jul 27, 2017
 #3
avatar+18621 
0

The three points (3,-5), (-a + 2, 3), and (2a+3,2) lie on the same line.

What is a?

 

Intercept theorem:

\(\begin{array}{|rcll|} \hline \dfrac{(2a-3)-(3)}{ 2-(-5) } &=& \dfrac{ (-a+2) - 3 } { 3-(-5) } \\\\ \dfrac{2a}{ 7 } &=& \dfrac{ -a -1 } { 8 } \\\\ 16a &=& -7a-7 \\ 23a &=& -7 \\ \mathbf{a} &\mathbf{=}& \mathbf{ -\frac{7}{23} } \\ \hline \end{array} \)

 

laugh

heureka  Jul 28, 2017

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