Find the incentre of a triangle formed by the points
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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})(paAx+bBx+cCx,paAy+bBy+cCy)
where, A_x\,,\,B_x\,,\,C_xAx,Bx,Cx are x coordinates of the vertex.
A_y\,,\,B_y\,,\,C_yAy,By,Cy 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})(39.911.7(7)+11.7(3)+16.5(−3),39.911.7(9)+11.7(−7)+16.5(3))=(39.981.9+35.1−49.5,39.69105.3−81.9+49.5)
=(\frac{67.5}{39.9},\frac{72.9}{39.9})=(1.7,1.8)=(39.967.5,39.972.9)=(1.7,1.8)
Therefore, Coordinates of the In center is ( 1.7 , 1.8 ).
Step-by-step explanation:
find the incentre of the triangle formed by the points A(7,9),B(3,-7),C(-3,3)
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