2d- Scaling Transformation

In simple words , scaling means an object can be viewed differently with various scales. An object with length 3cm might appear small when viewed with a scale in meters. Cars will appear bigger if you are looking down on the cars parked at a parking lot from 2nd floor of a building, but same set of cars will appear small from 8th floor of a building. Please notice what is object is not changing its size. Only distance , measurement scale is getting different.

A scaling transformation changes the size of an object. Sx and Sy are considered as scaling factors. If scaling factors have the value more than 1 then size of the object increases and if the values are low that 1 then compression happens.

If (x,y) are the coordinates of an object and (x’,y’) are the coordinates of transofrmed object then x’ and y’ after scaling is defined as follows.

x’=x.sx and y’=y*sy

The above two equations can be represented with matrix as:

Lets understand the concept of scaling by solving a numerical

Problem Statement:

Perform a scaling transformation on an object in square shape which is at coordinates A(0, 3), B(3, 3), C(3, 0), D(0, 0) with the scaling parameter as 2 towards X axis and 3 towards Y axis. also find new coordinates of the object.

S-1: In this case we have Point A with x1=0, y1=3, Point B with x2 =3 , y2 =3, Point C with x3=3 and y3=0, The last point or vertices D with x4=0 and y4=0. Scaling Parameters are given as Sx=2 and Sy=3.

S-2: The matrix in this case would be (3×4) , because of 4 corners of the square. The Matrix would be

S-3: After multiplication of above matrices the new coordinates after performing scaling transformation. A’=(0,6) B(6,9), C(6,0) and D(0,0)