Question

The coordinates of the vertices of a triangle are $A(-2,-2),B(3,1),C(-7,4).$ Find the coordinates of these vertices when the origin is shifted to the centroid of the triangle, the axes remaining parallel to the original axes.

Answer 1

Centroid $=\frac{A+B+C}{3}$ $=\frac{-2+3-7}{3},\frac{-2+1+4}{3}=\frac{-6}{3},\frac{3}{3}=(-2,1)$

origin is shifted to $(-2,1)$

$(h,k)=(-2,1)$

$(x_1,y_1)=(-2,-2)(x_2,y_2)=(3,1)(x_3,y_3)=(-y,y)$

$x_1=X_1+h$ $y_1=Y_1+k$

$X_1=x_1-h$ $Y_1=-2-1$

$=-2+2$ $=-3$

$X_1=0$

$\therefore$ , $(X_1,Y_1)=(0,-3)$

$X_2=x_2-h$ $Y_2=y_2-k$

$=3+2$ $Y_2=1-1$

$X_2=5$ $Y_3=3$ $(X_3,Y_3)=(-5,3)$

New verticles are $A=(0,-3)B=(5,0)C=(-5,3)$