Thread: IGCSE Maths Geometry Transformation

Triangle ABC, A(2,1) B(7,1) C(2,4); transform the triangle by the matrix(1 -1 next row 1 1) and the transformation is a rotation followed by an enlargement. How to calculate the angle of the rotation and the scale factor of the enlargement. Thank You..

I think this post belongs to university math, linear and advanced algebra.

I saw this in one of the IGCSE text...

Okay, I just thought you might get some answers easier there. Actually, I should know the answer but I guess I´ll have to admit, I forgot ho to do it

Good luck!

Originally Posted by wilbursmith

Okay, I just thought you might get some answers easier there. Actually, I should know the answer but I guess I´ll have to admit, I forgot ho to do it

Good luck!

A rotation matrix has the form
[cos x -sin x
sin x cos x ]
You can write your matrix as
sqrt(2) [ 1/sqrt(2) -1/sqrt(2)
............ 1/sqrt(2) 1/sqrt(2)]

Hence the angle of rotation is pi/4 radians, and the dilation factor is sqrt(2)

thank you sir;

Originally Posted by josemalawi

I saw this in one of the IGCSE text...

There is a way to derive the rotation geometrically without the use of linear algebra.

I did this some time ago for fun (sorry about the ironically wrong orientation of the attachment )