(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the quadrilateral (namely Q) in R^3 formed by the points

(1, 0, 0), (2, 0, 0), (1, 1, 3), and (2, 1, 3).

a) What should the coordinates be for the figure R we get by rotating Q counterclockwise in the x-y plane by 45 degrees, then dilating it by a factor of 3/2, then translating it along the vector (-2, 1, -1)?

b) Find the matrix that transforms Q into R.

3. The attempt at a solution

Okay, so what I did for (a) was I used the matrix

cosθ -sinθ 0

sinθ cosθ 0

0 0 1

Then substituted 45 for θ.

After this, multiplied the identity matrix for R^3 by 3/2 and then multiplied it by the matrix with 45 substituted for θ.

Then T(x,y,z) = (-2+3sqrt(2)x/4-3sqrt(2)y/4,1+3sqrt(2)x/4+3sqrt(2)y/4,-1+3z/2).

I substituted each of the quadrilateral points in for T(x, y, z) to come up with the four points and got:

(3/(2√2) - 2, 3/(2√2) + 1, -1),

(3/√2 - 2, 3/√2 + 1, -1),

(-2, 3/√2 + 1, 3.5),

(3/(2√2) - 2, 9/(2√2) + 1, 3.5)

I was wondering if someone could show me how to find the matrix that transforms Q into R. It would be greatly appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Transformation Matrix Problem

**Physics Forums | Science Articles, Homework Help, Discussion**