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Answer: 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.
