Question
(b) (i) Show that represents the equation of a line passing through (2, 3) and (−4, 7).
(ii) Prove that the equation of a line through and
can be
expressed in the form
Answer :
Word Count : 637
To solve these problems, let’s break them down step by step. ### Part (b)(i) We are asked to show that the determinant: \[ \begin{vmatrix} x & y & 1 \\ 2 & 3 & 1 \\ -4 & 7 & 1 \end{vmatrix} = 0 \] represents the equation of a line passing through the points \((2, 3)\) and \((-4, 7)\). #### Step 1: Evaluate the determinant The determinant of a 3x3 matrix is given by: \[ \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = a(ei - fh) - b(di - fg) + c(dh - eg) \] For our matrix: \[ \begin{vmatrix} x & y & 1 \\ 2 & 3 & 1 \\ -4 & _____ ______ __________ ______ ________ ________.
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To solve these problems, let’s break them down step by step. ### Part (b)(i) We are asked to show that the determinant: \[ \begin{vmatrix} x & y & 1 \\ 2 & 3 & 1 \\ -4 & 7 & 1 \end{vmatrix} = 0 \] represents the equation of a line passing through the points \((2, 3)\) and \((-4, 7)\). #### Step 1: Evaluate the determinant The determinant of a 3x3 matrix is given by: \[ \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = a(ei - fh) - b(di - fg) + c(dh - eg) \] For our matrix: \[ \begin{vmatrix} x & y & 1 \\ 2 & 3 & 1 \\ -4 & _____ ______ __________ ______ ________ ________.
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Related Questions
(c) Find the eccentricity, foci, centre and directrices of the ellipse Also give a rough sketch of it.
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(a) Let
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