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In a triangle ABC, if A is (1,2) and equation of the medians through B and C are x + y = 5 and x = 4 respectively, then B is : (1,4) (7,-2) (4,1) (-2,7)

In a triangle ABC, if A is (1,2) and equation of the medians through B and C are x + y = 5 and x = 4 respectively, then B is :
  1. (1,4)
  2. (7,-2)
  3. (4,1)
  4. (-2,7)

Grade:Select Grade

2 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
Hello student,
The equation of median through B is x+y = 5. The point B lies on it so the coordinates of B are (x1, 5-x1)
Now CF is a median through C, so coordiantes of F i.e. mid-point of AB are
((x1+1)/2, (5 – x1+ 2)/2)
Now this lies on x = 4 so this means (x1+1)/2 = 4
This gives x1 = 7
Hence, the cooridnates of B are (7, -2).
Kushagra Madhukar
askIITians Faculty 629 Points
10 months ago
Dear student,
Please find the solution to your problem below.
 
The equation of median through B is x + y = 5. The point B lies on it so the coordinates of B are (x1, 5 – x1)
Now the mid point of line joining AB will be ((x1+1)/2, (5 – x1+ 2)/2) → Let’s call this point F
Now F lies on the median through C
Thus it is satisfied by x = 4 
This means (x1+1)/2 = 4
This gives x1 = 7
Hence, the cooridnates of B are (7, – 2)
 
Thanks and regards,
Kushagra

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