PointHard
Question
If ᐃ1 is the area of the triangle formed by the centroid and two vertices of a triangle, ᐃ2 is the area of the triangle formed by the mid-points of the sides of the same triangle, then ᐃ1 : ᐃ2 =
Options
A.3 : 4
B.4 : 1
C.4 : 3
D.2 : 1
Solution
Let A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of a ᐃABC, and let G be its centroid.
Then,
ᐃ1 = Area of ᐃGBC
⇒ ᐃ1 =
, where ᐃ is the area of ᐃABC
ᐃ2 = Area of triangle formed by the mid-points of the sides
⇒ ᐃ2 =
ᐃ
∴ ᐃ1 : ᐃ2 = 4 : 3
Then,
ᐃ1 = Area of ᐃGBC
⇒ ᐃ1 =
, where ᐃ is the area of ᐃABCᐃ2 = Area of triangle formed by the mid-points of the sides
⇒ ᐃ2 =
ᐃ∴ ᐃ1 : ᐃ2 = 4 : 3
Create a free account to view solution
View Solution FreeMore Point Questions
Four points (x1, y1), (x2, y2), (x3, y3) and (x4, y4) are such that (x1x3 + x2x4 + y1y2 + y3y4)Then these points are ver...4 points out of 8 points in a plane are collinear. Number of different quadrilateral that can be formed by joining them ...The points with the co-ordinates (2a, 3a), (3b, 2b) & (c, c) are collinear -...The condition that three points (a, 0), (0, b) and (1, 1) are collinear is -...Coordinates of trisection of line joining points (−3, −3) and (6, 6) is -...