Math Is Fun Forum

Karuna

Guest

Linear transformations

Find the image of the triangle ABC with the vertices A(2,1),B(4,3),C(3,1) under a stretch, scale factor 2. with invariant line y=x

Bob

Administrator

Registered: 2010-06-20

Posts: 10,600

Re: Linear transformations

hi Karuna,

Welcome to the forum.

In a stretch the movement is perpendicular to the invarient line. For a scale factor of 2, points move away to twice the distance.

Hope that helps.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

rk_nithi

Novice

Registered: Today

Posts: 1

Re: Linear transformations

hi Karuna,

Welcome to the forum.

In a stretch the movement is perpendicular to the invarient line. For a scale factor of 2, points move away to twice the distance.

https://i.imgur.com/QqaD6h5.gif

Hope that helps.

Bob

Thanks for the feedback. Answer is correct. i would like to understand how to prove this with mathematical steps or equation? also can you tell me which software you are using to plot the graph?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,600

Re: Linear transformations

hi rk_nithi

Welcome to you as a new member!

Easy bit first. This is a vector graphics program called Geometer's Sketchpad.  There is also a free program called Geogebra which works similarly.  Geo is more versatile but takes longer to learn.  Sketchpad costs money but I got it years ago (before Geo) and it still serves me well. I like the control it gives over thickness of lines and colours.

Transformations that leave the origin invarient can be represented by a matrix transformation.  So, in theory there must be one for this one but I'll have to do a bit of work to find it.  I'll come back to this later.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob