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A line goes through (2,3),and (8,-2). The line has an X intercept of P and a y intercept of Q. Let the origin be O. Find the area of Triangle OPQ. 

 Jun 16, 2021
 #1
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Slope  =  (  -2 - 3)   / (8 - 2)  =  -5/6

 

Equation  of line   

 

y  = (-5/6) ( x  - 2)  +  3

 

y = (-5/6)x  +  5/3  +  3

 

y = (-5/6)x  +  14/3

 

Q =   (0,14/3)

 

To find P  

0  =  (-5/6)x  + 14/3

-14/3 =  (-5/6)x

(-14/3) ( -6/5)  = x =   28/5

 

The  area of  the triangle   =   (1/2) (28/5) ( 14/3)    =  196/15  units^2  ≈   13.07 units^2

 

 

cool cool cool

 Jun 16, 2021

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