Not sure how to proceed. Maybe unit circle trig?:
A line in the coordinate plane has a slope of 4 and a distance of 1 unit from the origin. Find the area of the triangle determined by the line and the coordinate axes.
Thanks Much! 
Locate that line so that it crosses the X-axis at –1 .... the slope of +4 causes the line to cross the Y-axis at +4.
That creates a right triangle with a base of 1 unit and a height of 4 units. It should be easy to figure the area.
It would work at X=+1 as well, it's just easier to visualize the triangle if you use the Y-axis as one leg.
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+500 Hey guest!
I'm not really sure what the question means when the line has a distance of 1 unit from the origin. Does that mean the y intercept or x intercept, or what exactly? If it means that the line stops at 1 unit from the origin, that would just be a vector, so I'm not really sure what the question is asking here. If you have any ideas, feel free to lmk!
If this is difficult for you to visualize mentally, then draw it.
Draw four X-Y coordinate planes.
Put a dot on each axis 1 unit from the origin. The origin is where the axes cross.
Through each dot, draw a line with slope 4. Slope 4 means the line goes up 4 for every 1 it goes to the right.
My post accounted for two of the triangles. I should have drawn them, cuz I neglected to mention the other two.
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Hi all. The question is asking to find the area of the triangle in this diagram. Ignore the decimal values, I just wrote those to help visualize. The right triangle formed by the two axes and the line. As you can see, It will not be a whole number. {https://www.desmos.com/calculator/xq3u4ubj6x} This link is my diagram. Again, it is just to help visualize.
Thanks for replying other guest, but the triangle is not just a right triangle with base 1 and height 4. I thought that at first but sadly, that is too simple. I still need help.
+2094 Since we know that the slope is 4, we can narrow done the possible side lengths.
Also, we know that the line is 1 unit from the origin.
That will create a right triangle with a height of 4 and a base of 1. Therefore, the area is 4.
Hope this helped!
