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

 Jan 30, 2021
edited by Guest  Jan 30, 2021
edited by Guest  Jan 30, 2021
 #1
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+1

The slope  between  any  two points  is  constant

 

Therefore

 

Slope  between first two points =  slope  between  first and  third  point

 

(3 -  - 5)  / ( -a + 2 - 3)    = (2 - - 5)  /( 2a + 3  -  3)      simplify

 

(8) / ( -a - 1)   =   ( 7)  / ( 2a)     cross-multiply

 

8 * 2a  = 7 (-a - 1)

 

16a  =  -7a  - 7     add 7a to  both sides

 

23a  =  -7 

 

a =  -7/23

 

 

cool cool cool

 Jan 30, 2021

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