Question

Foundations of Geometry Course!!

17. Write a brief essay (1 page: introduction, development and conclusion) in which you describe how to find a matrix formula for a reflection about the line whose equation is y 3x- 4.

Answer 1

Given data A bries essay (1 page introduction) development and conclusion in which you descrives how to find a matrix formula for a resection about me line whose equation is y = 3x - 4 y = 3x + b 1 traslate by (0, -6) so mat line y = mx + b maps to you I emx + b rightarrow mx 2. Reflect through me line y = mx using me known formula (matrix formula Translate (0, b) to undo me earlier tramssorimation) Development the translation matrices are, respectiovely (1 0 0 1 -b 0 0 1) and (1 0 0 0 1 b 0 0 1) and me matrix so me reslection about y = mx is \r\n 1/1 + m^2 (1 - m^2 2m 0 2m m^2 - 1 0 0 0 1 + m^2) Applying these in me correct sequence, me trans formation is 1/1 + m^2 (1 0 00 0 1 b 0 0 1) (1 - m^2 2m 0 2m m^2 - 1 0 0 0 1 + m^2) (1 0 0 0 1 -b 0 0 1)