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2: Show that the line equation passing through two distinct points (a1, b1) and (a2, b2) can be given as T y 1 a1 bi 1= 0. a2 b2 1

2: Show that the line equation passing through two distinct points (a1, b1) and (a2, b2) can be given as T y 1 a1 bi 1= 0. a2 b2 1

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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2: Show that the line equation passing through two distinct points \((a_1, b_1)\) and \((a_2, b_2)\) can be given as \[ \begin{vmatrix} x & y & 1 \\ a_1 & b_1 & 1 \\ a_2 & b_2 & 1 \\ \end{vmatrix} = 0. \] This expression represents the determinant of a 3x3 matrix. When expanded, the determinant provides the equation of the line passing through the given points. The condition \(= 0\) ensures that the point \((x, y)\) lies on the line defined by the points \((a_1, b_1)\) and \((a_2, b_2)\).
Transcribed Image Text:2: Show that the line equation passing through two distinct points \((a_1, b_1)\) and \((a_2, b_2)\) can be given as \[ \begin{vmatrix} x & y & 1 \\ a_1 & b_1 & 1 \\ a_2 & b_2 & 1 \\ \end{vmatrix} = 0. \] This expression represents the determinant of a 3x3 matrix. When expanded, the determinant provides the equation of the line passing through the given points. The condition \(= 0\) ensures that the point \((x, y)\) lies on the line defined by the points \((a_1, b_1)\) and \((a_2, b_2)\).
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