Math, linear algebra, electrical engineer

Question

Hi, I need some help with some mathematical problems.

Question 1.

A line segment PQ have the coordinates P=[1,3] and Q=[4,3]. The new transformed line segment P'Q' emerges by reflecting PQ around the line given by y = - ( sqrt ( 3 ) / 3 ) x + 1

a) Find the simple standard matrix to all necessary transformations and find the standard matrix to the compound transformation.

b) find the coordinates to the new line segment P'Q' and draw PQ and P'Q' with the line

y = - ( sqrt ( 3 ) / 3 ) x + 1

Answer 1

Look Jorgen H.,

You're taking a high-level course in linear algebra, so you should already know how to approach a problem like this: sketch it first! ???

Rapidly, you will see that the stated line has a particular y-intercept (1) and a particular slope (-1/(3)^0.5), and that the initial segment PQ is lying above that. So, a matrix transformation is intended to move both x and y (of your initial segment) to the reflected positions (it's not a rotation, you aren't using 3-space). Right away, you can tell that: any movement is perpendicular to the stated line, so that gives you the "slope" of the point movement (-1/(-1/(3)^0.5))) = 3^0.5 ; also, the distance moved depends on the distance to that line AS MOVED (so you must solve the Pythagorean distance thing), and then again the same distance on the other side.

There's nothing tricky here, but there are some calculations. I won't advise you on the matrix bit, your matrix notation is fresher than mine.

-- Cheers, --Mr. d.