Question

20.
In a A ABC, A (4,2) and D0.1 such that AD is median then its centroid
is
[ ]​

Answer 1

Step-by-step explanation:

Given:-

In a A ABC, A (4,2) and D(0,1) such that AD is median

To find:-

Find its centroid ?

Solution:-

Given points are A (4,2) and D(0,1)

and given that

AD is the median in ∆ABC

We know that The concurrent point of medians in a triangle is called its centroid.

The centroid divides the median in the ratio 2:1

So,AG :GD = 2:1

Let the Centroid be G(x,y)

Let m:n = 2:1 =>m = 2 and n = 1

and

Let (x1, y1)=A(4,2)=>x1=4 and y1 =2

Let (x2, y2)=D(0,1)=>x2=0,y2=1

We know that

The section formula

The Coordinates of the point which divides the linesegment joining the points A (x1, y1) and

B(x2, y2) in the ratio m:n is

[(mx2+nx1)/(m+n),(my2+ny1)/(m+n)]

On Substituting these values in the above formula

=>G(x,y)=[(2×0+1×4)/(2+1),(2×1+1×2)/(2+1)]

=>G(x,y)=[(0+4)/3,(2+2)/3]

=>G(x,y)=(4/3,4/3)

The Centroid = (4/3,4/3)

Answer:-

Required Centroid for the given problem is (4/3,4/3)

Used formulae:-

• .The concurrent point of medians in a triangle is called its centroid.
• The centroid divides the median in the ratio 2:1
• The Coordinates of the point which divides the linesegment joining the points A (x1, y1) and
• B(x2, y2) in the ratio m:n is
• [(mx2+nx1)/(m+n),(my2+ny1)/(m+n)l