Question

AD is median of triangle ABC , where coordinates of B and C are respectively (4,1) and (1,6) then coordinates of D are??

Answer 1

Answer:

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Step-by-step explanation:

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  ,  2s+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)