+0

+5
7
796
3
+737

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

Jul 27, 2017

#1
0

Don't be a fat fu*k

Jul 27, 2017
#2
+7352
+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

Jul 27, 2017
#3
+21869
0

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

What is a?

Intercept theorem:

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

Jul 28, 2017