Question

prove that the area
is invariant under
of
the
the triangle
translation of
the
axes.
​

Answer 1

Let the original coordiantes of vertices of △ABC are, Ax1,y1, Bx2,y2, Cx3,y3Then the area of △ABC is given by, Area△ABC=12x1y2-y3+x2y3-y1+x3y1-y2 .....1Now suppose that the origin O0,0 is shifted to new position O'h,kThen the new coordinates of triangle are given by, A'x1+h,y1+k, B'x2+h,y2+k, C'x3+h,y3+kUse formula in 1 to find the area of new triangle. Area△A'B'C'=12x1+hy2+k-y3+k+x2+hy3+k-y1+k+x3+hy1+k-y2+k =12x1+hy2+k-y3-k+x2+hy3+k-y1-k+x3+hy1+k-y2-k =12x1+hy2-y3+x2+hy3-y1+x3+hy1-y2 =12x1y2-y3+hy2-y3+x2y3-y1+hy3-y1+x3y1-y2+hy1-y2 =12x1y2-y3+x2y3-y1+x3y1-y2+hy2-y3+y3-y1+y1-y2 =12x1y2-y3+x2y3-y1+x3y1-y2+h0 =12x1y2-y3+x2y3-y1+x3y1-y2+0 =12x1y2-y3+x2y3-y1+x3y1-y2 =Area △ABCThis proves that area of triangle is invariant under translation of axis

hope it helped you

please mark brainly