This problem on co-ordinate geometry is from AMC 10B, 2019. First try it yourself.
All lines with equation ax+by= c such that a,b,c form an arithmetic progression pass through a common point . What are the coordinates of that point?
Arithmetic Progression
2D - Co- ordinate Geometry
Cartesian System of Points
Answer: (-1,2)
AMC 10B - 2019 - Problem No - 4
Challenges and Thrills in Pre-College Mathematics
If all lines satisfy the condition, then we can just plug in values for a,b,c that form an arithmetic progression. Let's use a =1,b= 2,c=3 and a= 1,b=3,c =5. Then the two lines we get are:
x+2y =3
x+3y = 5 so
y= 2
Now plug the value of y into one of the previous equations. We get :
x+4=3
x = -1
Ans is (-1,2)
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