Rotating Points using a Matrix

[Al Borland]

I'm having issues with an assignment my teacher gave me. I thought I had everything going well until I plotted it out. I found that my coordinates for the plotted points turned into an entirely different shape instead of just rotating it.

Here is the problem that I was requested to do:

On paper, draw the “house” object defined by the 5 points:
(-1,0), (1,0), (1,2), (0,3) and (-1,2).

Then do the following steps by hand:
a. Write down the matrices R and T that apply a rotation by 60º and a translation
by <4, 2> respectively.

b. Apply R to each point, and then with the result of this first multiplication, apply
T. i.e. For each point, calculate p’ = Rp and graph the result as accurately as you
can. Then calculate p’’ = Tp’ for each of the points you just calculated, and
graph the result. Your graph should show three versions of the house.

For Part A i created the matrix

R = { xcos(60) - ysin(60) }
{ xsin(60) + ycos(60) }
as far as I know for non homogeneous lines this is what we do. The plot points I get for reach one keep turning out wrong though and not maintaining a shape. I went through all my points again and came up with the same answer for each point's value.

Can anyone help me figure out where I am going wrong here?

 

[mmm4444bot]

R = { xcos(60º) - ysin(60º) }
{ xsin(60º) + ycos(60º) }

This is not matrix R.

Instead, this is what you get after matrix multiplication of R times an original point (x, y).

Remove the variables x and y from your matrix above.

In other words, after rotating the coordinate system 60º, the coordinates of the new points (X, Y) are:

X = x cos(60º) - y sin(60º)

Y = x sin(60º) + y cos(60º)

I applied the rotation, and I get the image below.

 

[Al Borland]

Thanks that really clears it up.

 

[Al Borland]

okay I am having an issue here when i try to input in (3,0) I'm not getting the same last coordinate here as you are mine is giving me like (1.5, 2.5) whats going on here?

 

[Al Borland]

Sorry for the multiple posts but i cant see and edit them till they are approved. I figured out what I was doing wrong i reversed the (0,3) and made it (3,0) for some reason.