SOLUTION: Use a determinant to find an equation of the line passing through the points (x, y). (−2, 5), (4, 1)

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Question 1179373: Use a determinant to find an equation of the line passing through the points
(x, y).
(−2, 5), (4, 1)
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.


                It can be done in different ways.

                I will show and explain one of them to you,  the most simplest,
                which you can,  probably,  will remember and understand all your life. 


You have two vectors with components


    (4-(-2), 1 - 5) = (6,-4)    (starts at (-2,5),  ends at (4,1) )

and

    (x-4,y-1)                   (starts at (4,1);  ends at (x,y) )



        You want these two vectors be parallel (or antiparallel, does not matter).



It means that the determinant, composed of the components of these vectors is equal to zero


    det  = 0.                ANSWER


It is your equation, same as


    -4*(x-4) - 6*(y-1) = 0.     (*)      ANSWER


You can simplify the resulting equation (*) any way as you want.

Solved, explained and completed.



Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
Use a determinant to find an equation of the line passing through the points
(, )
(,), (, )



let (,) be (,) and
(,) be (, )





....simplify

-> answer


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