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Question:

OA: y= 4x

AB: 3y+8x=400

OB: y=0

Find the Coordinates of A and B

I am really not sure how to do this problem.

I've tried using system of equations to see which numbers will have in common between O, A and B. But I was honestly guessing which method could work. Could someone help me on this problem?

Thanks!

Holdstill 123
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2 Answers2

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The point $A$ is the intersection of $OA$ and $AB$. To find $A$, we solve the linear equation system $y = 4x$ and $3y + 8x = 400$. Inserting the first equation into the second one, you get $12x + 8x = 400$, which is $x = 20$. Hence $A$ has the coordinates $(20, 80)$.

Similarly, to find the point $B$, we solve the linear equation system $3y + 8x = 400$ and $y = 0$ and get $x = 50$. Hence $B$ has the coordinates $(50,0)$.

Jordan
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Your problem is

A is at $OA=AB$.

That is $4 x= (400-8x)/3=400/3-8 x/3$. $20 x/3=400/3$ or $20 x=400$ or $x=20$. $y=(400-8x)/3=(4000-8*20)/3=80$.

So A is the point, coordinate tuple A=$(20,80)$.

B is at $OB=AB$.

That is $0=(400-8x)/3$. $0=400-8x$ or $x=50$.

So B is the point, coordinate tuple B=$(50,0)$.

The solution in a plot is:

enter image description here

Steffen Jaeschke
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  • How would I find the area of that triangle? – Holdstill 123 Mar 18 '21 at 10:55
  • This is composed out of two rectangular triangles. One is O(20,0)A, the other is (20,0)B,A. The both follow the formular ab/2. So the left area is 800 and the right is 1200. Both. add up to the area enclosed by OBA of 2000. – Steffen Jaeschke Mar 19 '21 at 16:10