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A line has slope 2. Find the area of the triangle formed by this line and the coordinate axes, if the distance between the origin and the line is 5

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 Dec 3, 2023
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The PERPINDICULAR line from the origin has a slope of   - 1/m =  -1/2 

  so  this line is  y = - 1/2 x 

   A circle of radius 5 , centered at the origin (  x^2 + y^2 = 5^2 ) 

    Intersects are prpindicular line at   (4.472 , -2.236) 

        NOW....the equation of the line that contains THIS point and has a slope of 2 is 

                     y + 2.236 = 2 ( x - 4.472) 

                   or  y = 2x - 11.18 

 

This has a y-axis intercept of  - 11.18    and the x intercept is 5.59 

Area of the triangle is 1/2 base * height     

     = 1/2   * 11.18  * 5.59 =  31.25 units^2 

Here is a Desmos graph showing all of this :

 Dec 5, 2023

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