Answer:

Coordinates of the In center is ( 1.7 , 1.8 ).

Step-by-step explanation:

Given: Coordinates of the triangle A( 7 , 9 ) , B( 3 , -7 ) and C( -3 , 3 )

To FIND: In center of the triangle.

In center of the triangle = (\frac{a\,A_x+b\,B_x+c\,C_x}{p},\frac{a\,A_y+b\,B_y+c\,C_y}{p})(

p

aA

x

+bB

x

+cC

x

,

p

aA

y

+bB

y

+cC

y

)

where, A_x\,,\,B_x\,,\,C_xA

x

,B

x

,C

x

are x coordinates of the vertex.

A_y\,,\,B_y\,,\,C_yA

y

,B

y

,C

y

are y coordinates of the vertex.

a , b , c are the LENGTH of sides opposite to vertex A , B and C respectively.

p is the perimeter of the triangle.

length of the side AB opposite to vertex C , c = \sqrt{(3-7)^+(-7-9)^2}=\sqrt{16+256}=16.5

(3−7)

+

(−7−9)

2

=

16+256

=16.5

length of the side CB opposite to vertex A , a = \sqrt{(-3-3)^+(3-(-7))^2}=\sqrt{36+100}=11.7

(−3−3)

+

(3−(−7))

2

=

36+100

=11.7

length of the side AC opposite to vertex B , b = \sqrt{(-3-7)^+(3-9)^2}=\sqrt{100+36}=11.7

(−3−7)

+

(3−9)

2

=

100+36

=11.7

p = 11.7 + 11.7 + 16.5 = 39.9

So, In center

(\frac{11.7(7)+11.7(3)+16.5(-3)}{39.9},\frac{11.7(9)+11.7(-7)+16.5(3)}{39.9})=(\frac{81.9+35.1-49.5}{39.9},\frac{105.3-81.9+49.5}{39.69})(

39.9

11.7(7)+11.7(3)+16.5(−3)

,

39.9

11.7(9)+11.7(−7)+16.5(3)

)=(

39.9

81.9+35.1−49.5

,

39.69

105.3−81.9+49.5

)

=(\frac{67.5}{39.9},\frac{72.9}{39.9})=(1.7,1.8)=(

39.9

67.5

,

39.9

72.9

)=(1.7,1.8)

THEREFORE, Coordinates of the In center is ( 1.7 , 1.8 )