A(-1,3), B(5,2) and C(5,-2) arethe vertices of a triangle. (i)Find the coordinates of thecentroid G of the triangle(ii)Find the equation of the linethrough G and parallel to AC *. Created by suhan03. Math

Step-by-step explanation:ANSWERGiven, A(−1,3),B(4,2),C(3,−2)(i) Co-ordinates of centroid G is G(x,y)=( 2(x 1 +x 2 +x 3 ) , 2(y 1 +y 2 +y 3 ) )=( 3(−1+4+3) , 3(3+2−2) )=( 36 , 33 )=(2,1)Hence, the co-ordinates of the centroid G of the triangle is (2,1)(ii) Slope of AC= (x 2 −x 1 )(y 2 −y 1 ) = (3−(−1))(−2−3) = 4−5 So, the slope of the line parallel to AC is also 4−5 Now, the equation of line through G is y−1=( 4−5 )(x−2)4y−4=−5x+105x+4y=14Thus, the required line equation 5x+4y=14.