Question

find the incentre of the triangle formed by the points A(7,9),B(3,-7),C(-3,3)

Answer 1

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Answer 2

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 = $(\frac{a\,A_x+b\,B_x+c\,C_x}{p},\frac{a\,A_y+b\,B_y+c\,C_y}{p})$

where, $A_x\,,\,B_x\,,\,C_x$ are x coordinates of the vertex.

$A_y\,,\,B_y\,,\,C_y$ 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 = $\sqrt{(3-7)^+(-7-9)^2}=\sqrt{16+256}=16.5$

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

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

p = 11.7 + 11.7 + 16.5 = 39.9

So, In center

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

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

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