Question

In a ΔABC, if A is the point (1, 2) and equations of the median through B and C are respectively x + y = 5 and x = 4, then B is​

Answer 1

Answer

ΔABC has vertex A(1,2)

Given that midpoint of AC is D and mid point of AB is E

Also,

equation of medium BD is x+y=5

equation of medium CE is x=4

let coordinate of B(p,q) and C(r,s)

∴ coordinate of E≡(

2

p+1

,

2

q+1

)

But E lies on the line segment CE (x=4)

∴

2

P+1

=4

⇒P=7

And point B(p,q) lies on the line BD [x+y=4]

∴ p+q=4

⇒q=−3

∴ B≡(7,−3)

Point C(r,s) lies on CE [x=4]

∴ r=4

Coordinates of D are ≡[

2

r+1

,

2

s+2

]

Similarly point D lies on BD [x+y=5]

∴

2

r+1

+

2

s+2

=5

r+s=7

⇒s=3

∴ C≡(4,3)

∴ coordinates of B & C are (7,−3) & (4,3)

Answer 2

Answer:

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