Parallelogram abcd has vertex coordinates a(0,2) b (6,2) c (8,6 and d (2,6) write a rule to find the vertex coordinates of a parallelogram pqrs that is smaller than , but similar to abcd

 The rule is explained.

Step-by-step explanation:  As shown in the attached figure, ABCD is a parallelogram with vertices A(0,2), B(6,2), C(8,6) and D(2,6).

Suppose, we are to find the vertices of a parallelogram PQRS that is smaller than but similar to ABCD, then we can follow the following rule.

Let us consider a positive real number k. Then the new coordinates of smaller and similar parallelogram PQRS will be

Co-ordinates of P will be (k,2+k),

Co-ordinates of Q will be (6-k,2+k),

Co-ordinates of R will be (8-k,6-k)

and

co-ordinates of S will be (2+k,6-k).

Taking any positive real value of k, we will get a new, smaller parallelogram which will be similar to ABCD.