The correct option is
B (7,−3),(4,3)
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≡(p+12,q+12)
But E lies on the line segment CE (x=4)
∴ P+12=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 ≡[r+12,s+22]
Similarly point D lies on BD [x+y=5]
∴ r+12+s+22=5
r+s=7
⇒s=3
∴ C≡(4,3)
∴ coordinates of B & C are (7,−3) & (4,3)
![1179623_1304019_ans_90a342a01f8a42ceab65d6a0b2e1cacb.jpg](https://search-static.byjusweb.com/question-images/toppr_ext/questions/1179623_1304019_ans_90a342a01f8a42ceab65d6a0b2e1cacb.jpg)