Math, asked by peddialekhya, 5 months ago

Let A(4,2), B(6,5) and C(1,4) be the vertices of AABC
1. The median from Ameets BC at D. Find the coordinates of the
point D
3. Find the points which divide the line segment BE in the ratio 2:1 and also that divide the
2:1
line segment CF in the ratio 2:1
2. Find the coordinates of the point Pon AD such that AP: PD-
4. What do you observe?
Justify the point that divides each median in the ratio 2 : 1 is the centriod of a triangle​

Answers

Answered by ABSuryashankar
1

Answer:

i)

Median is the line joining the midpoint of one side of a triangle to the opposite vertex. So, the coordinates of D would be(

2

6+1

,

2

5+4

)::(

2

7

,

2

9

)

ii)

P divides AD in the ratio 2:1.

A(x

1

,y

1

)=(4,2), D(x

2

,y

2

)=(

2

7

,

2

9

)

m:n=2:1

Using section formula, we get the coordinates of P.

P(x,y)=(

m+n

nx

1

+mx

2

,

m+n

ny

1

+my

2

)

=

2+1

1⋅4+2⋅

2

7

,

2+1

1⋅2+2⋅

2

9

=(

3

11

,

3

11

)

iii)

Coordinates of E will be (

2

5

,3) and the coordinates of F=(5,

2

7

).

Coordinates of Q=(

m+n

nx

1

+mx

2

,

m+n

ny

1

+my

2

)

=

2+1

1⋅6+2⋅

2

5

,

2+1

1⋅5+2⋅3

=(

3

11

,

3

11

)

Coordinates of R=(

m+n

nx

1

+mx

2

,

m+n

ny

1

+my

2

)

=

2+1

1⋅1+2⋅5

,

2+1

1⋅4+2⋅

2

7

=(

3

11

,

3

11

)

iv)

The coordinates of P,Q and R are the same which is (

3

11

,

3

11

).

This point is called the centroid, denoted by G.

v)

Centroid of triangle ABC=(

3

x

1

+x

2

+x

3

,

3

y

1

+y

2

+y

3

)

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