# Graph of a Relation under a Linear Coordinate Transformation

Graph of a Relation under a Linear Coordinate Transformation

Suppose a graph of a relation in two variables is given, and a relation is defined by

P

R

R(X,Y)⇔P(a(X-b),c(Y-d))

Then the point is on the graph of iff the point is on the graph of , and .

(X,Y)

R

(x,y)=(a(X-b),c(Y-d))

P

(X,Y)=(x/a+b,y/c+d)=(x/a,y/c)+(b,d)

So to get the graph of , the graph of is scaled by and translated by .

R

P

(1/a,1/c)

(b,d)