Question

21. If a vertex of a triangle is (1, 1) and the midpoints of two sides of the triangle through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is
A. `(-1/3, 7/3)`
B. `(-1, 7/3)`
C. `(1/3, 7/3)`
D. `(1, 7/3)`

Answer 1

Correct Answer - D
Midpoint of `AB=(-1, 2)`
`implies ((x_(2)+1)/2, (y_(2)+1)/2)=(-1, 2)`

`implies (x_(2)+1)/2=-1, (y_(2)+1)/2=2`
`implies x_(2)+1=-2, y_(2)+1=4`
`implies x_(2)=-3, y_(2)=3`
Midpoint of `AC=(3, 2)`
`implies ((x_(1)+1)/2, (y_(1)+1)/2)=(3, 2)`
`implies x_(1)+1=6, y_(1)+1=4`
`implies x_(1)=5, y_(1)=3`
So, vertices of triangle ABCare (1, 1), (-3, 3), (5, 3)
So, centroid `=((1-3+5)/3, (1+3+3)/3)=(3/3, 7/3)=(1, 7/3)`