Question

In a triangle ABC the midpoint of BC is (2,1) and the centroid (0,3) . The vertex A is
A. (2, 4)
B. (4, -7)
C. (-4, -7)
D. (-4, 7)

Answer 1

coordinate of centroid=

(x1+x2+x3)/3=. 0 => x1+x2+x3= 0 .........,...(1)

(y1+y2+y3)/3= 3 => y1+y2+y3= 9 .............(2)

again coordinate of mid pint of BC

(x2+x3) /2= 2 => x2+ x3= 4 ......,......(3)

( y2+y3)/ 2= 1 =>. y2+y3= 2 ............(4)

from (1) and (3)

x1= 0-4= - 4

from (2) and (4)

y1= 9-2= 7

therefore coordinate of A: ( -4 7)

option (D) is correct