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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  \(8\)

 Apr 21, 2022
 #2
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Deleted

 Apr 21, 2022
edited by Alan  Apr 21, 2022
 #3
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Find the area of the triangle.

 

Hello Guest!

 

\(Touch\ Point\ P:\\ x_P=8\cdot cos(atan -\frac{1}{2})=7.155\\ y_P=8\cdot sin(atan -\frac{1}{2})=-3.578\\ f(x) =2\cdot (x-x_P)+y_P\\ f(x)=2x-2\cdot 7.155-3.578\\ f(x)=2x-17.888=0\\ P_x\ (8.944,0)\\ P_y(0,-17.888)\)

The area of this triangle is

\(A_{xy}=\frac{1}{2}\cdot 8.944\cdot (-17.888)\)

\(A_{xy}=-79.995\)

laugh  !

 Apr 21, 2022
edited by asinus  Apr 21, 2022

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