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A line with slope 3 is 4 units away from the origin. Find the area of the triangle formed by this line and the coordinate axes.

 Nov 25, 2020
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The line will have  the  form  y = 3x  + b

 

In standard form we have   3x - y  + b = 0

 

Using the  formula for the distance  from a point to a line  we can solve for b thusly  :

 

l  3(0) - 0  + b l

______________    =   4

sqrt ( 3^2 + 1^2)

 

 

   b

________   =   4

sqrt (10)

 

 

b = 4 sqrt (10) =    the height of the triangle

 

So  the eqation of the  line is

 

y = 3x  +  4sqrt (10)

 

Letting   y = 0, we can find  the base of the triangle  as

 

3x = -4sqrt (10)

 

x =    -(4/3)sqrt (10)

 

The absolute value of this is the base length

 

So....area of the triangle  is

 

(1/2)  (base) (height)  =

 

(1/2) (4/3)sqrt (10) (4 sqrt (10)  = 

 

(1/2) ( 4/3) ( 4) ( 10)  =

 

80/3  units^2

 

 

cool cool cool

 Nov 26, 2020

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