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Consider point P(x, y) in first quadrant. Its reflection abou x-axis is Q(x₁, y₁). So, x₁ = x and y₁ = -y. x₁ = 1. x + 0.y This may be written as: y₁ = 0. x + (-1) y This system of equations can be put in the matrix as:

Consider point P(x, y) in first quadrant. Its reflection abou x-axis is Q(x₁, y₁). So, x₁ = x and y₁ = -y. x₁ = 1. x + 0.y This may be written as: y₁ = 0. x + (-1) y This system of equations can be put in the matrix as:

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider point P(x, y) in first quadrant. Its reflection about x-axis is Q(x₁, y₁). So, x₁ = x and y₁ =-y. [ x₁ = 1.x +0. y ₁0. x + (-1) y = This may be written as: This system of equations can be put in the matrix as: X1 [l- l [1 Here, matrix 1 0 X 0 -1 is the matrix of reflection about x-axis. Then find the matrix of (i) reflection about y-axis (ii) reflection about the line y = x (iii) reflection about origin (iv) reflection about line y = (tan 0)x
Transcribed Image Text:Consider point P(x, y) in first quadrant. Its reflection about x-axis is Q(x₁, y₁). So, x₁ = x and y₁ =-y. [ x₁ = 1.x +0. y ₁0. x + (-1) y = This may be written as: This system of equations can be put in the matrix as: X1 [l- l [1 Here, matrix 1 0 X 0 -1 is the matrix of reflection about x-axis. Then find the matrix of (i) reflection about y-axis (ii) reflection about the line y = x (iii) reflection about origin (iv) reflection about line y = (tan 0)x
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