Question

verify that distance between the vertices of a triangle remain unchanged under any displacement and rotation of the triangle

Answer 1

Answer:

Displacement Does not change distance between vertex of triangle

Step-by-step explanation:

Let say co-ordinates of triangles  ABC

are A ( Ax  , Ay)  

      B (Bx  , By)

      C  (Cx , Cy)

AB = √{(Ax - Bx)² + (Ay - By)²}

AC = √{(Ax - Cx)² + (Ay - Cy)²}

BC = √{(Bx - Cx)² + (By - Cy)²}

now let say Displacement is Done Dx in x - axis   & Dy  in y - axis

then new co-ordinates rae

A'  = (Ax + Dx) , (Ay + Dy)

B'  = (Bx + Dx) , (By + Dy)

C'  = (Cx + Dx) , (Cy + Dy)

A'B' = √{(Ax + Dx - (Bx+Dx))² + (Ay+Dy - (By+Dy))²}

=> A'B' = √{(Ax - Bx)² + (Ay - By)²} = AB

A'C' = √{(Ax + Dx - (Cx+Dx))² + (Ay+Dy - (Cy+Dy))²}

=> A'C'  = √{(Ax - Cx)² + (Ay - Cy)²} = AC

B'C' = √{(Bx + Dx - (Cx+Dx))² + (By+Dy - (Cy+Dy))²}

=> B'C' = √{(Bx - Cx)² + (By - Cy)²} = BC

Hence its Clear that Displacement Does not change distance between vertex of triangle