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# Coordinates

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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

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Deleted

Apr 21, 2022
edited by Alan  Apr 21, 2022
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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

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

$$A_{xy}=-79.995$$

!

Apr 21, 2022
edited by asinus  Apr 21, 2022