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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! smiley

 Mar 21, 2020
 #1
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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.

.

 Mar 21, 2020
 #2
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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!

 Mar 21, 2020
 #4
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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. 

.

Guest Mar 21, 2020
 #3
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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.

 Mar 21, 2020
 #5
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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.

 Mar 21, 2020
 #6
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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!

 Mar 21, 2020
 #7
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Sorry, but that isn't right. I already tried it. Halp!

 Mar 21, 2020
 #8
avatar+1956 
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Really? I will try to work it out more.... Sorry about that!

CalTheGreat  Mar 21, 2020
 #9
avatar+30038 
+2

"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."

 

 Mar 21, 2020
 #10
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That is right Alan!!! Thank you very much. That is a great explanation. I guess I was overcomplicating. Also, thank you other posters. I love this site so much! laughsmileylaugh

Guest Mar 21, 2020

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