# analytic geometry helps are appreciated

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A line with slope 3 is 2 units away from the origin. Find the area of the triangle formed by this line and the coordinate axes.

How is this even going to be done? We are given little info but a bunch of variables. Could someone help please??

• analytic geometry helps are appreciated -

So the "legs" of the triangle would be 2 I believe. And the area of a triangle is (Length*Width)/2. So I think the area should be 2units^2. I'm not sure if that's what you were asking.

• analytic geometry helps are appreciated -

The line can pass by the origin on the right or the left, but the answer will be the same. The sloped line will be the hypotenuse of a triangle whose other two sides are segments of the x or y axes, ending at the origin.

The angles of the triangle are 71.56 degrees (arctan3), 90 degrees, and 18.44 degrees.

The length of the side opposite the small angle is 2/sin18.44 = 6.32

The length of the hypotenuse is
6.32/cos18.44 = 6.66

The area of the triangle =
(1/2)*(hypotenuse)*(height)
= 4.44 square units

• analytic geometry(correction) -

I must have punched some wrong keys on my calculator

The area of the triangle is
(1/2)*(hypotenuse)*(height)
= 6.66 square units

since the height (distance of the line from the origin) is 2 units.

• analytic geometry helps are appreciated -

thank you very much it helps a lot!!!

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