If c (-1,k) is a point on the line passing through the points A(2,4) and B(4,8) which number is K

Question

If c (-1,k) is a point on the line passing through the points A(2,4) and B(4,8) which number is K

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Eden 1 month 2021-10-22T00:14:44+00:00 1 Answer 0 views 0

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    2021-10-22T00:15:51+00:00

    Question :

    If C(-1,k) is a point on the line passing through the points A(2,4) and B(4,8) then find which number is K.

    ANSWER :

     \\  \to {  \boxed { \bold{k  =  - 2 }}} \\

    EXPLANATION :

    GIVEN :

    A point C(-1,k) passing from a line which is passing through the points A(2,4) and B(4,8).

    TO FIND :

    • Value of k’.

    SOLUTION :

    ▪︎First , we have to find a line which is passing from A(2,4) and B(4,8).

    ▪︎ We know that –

    Equation of line which is passing from (a,b) and (c,d) is –

     \\  \implies { \boxed{ \bold{(y - b) =[ \dfrac{(d - b)}{(c - a)}](x -  a)}}} \\

    • Here –

     \\  \:  \:  \:  \:  \:  \:  \: . \:  \:  \:  { \bold{a = 2}}\\

     \\  \:  \:  \:  \:  \:  \:  \: . \:  \:  \:  { \bold{b = 4}}\\

     \\  \:  \:  \:  \:  \:  \:  \: . \:  \:  \:  { \bold{c = 4}}\\

     \\  \:  \:  \:  \:  \:  \:  \: . \:  \:  \:  { \bold{d = 4}}\\

    • Now put the values –

     \\  \implies { \bold{(y - 4) =[ \dfrac{(8 - 4)}{(4 -  2)}](x -  2)}} \\

     \\  \implies { \bold{(y - 4) = \dfrac{4}{2}(x -  2)}} \\

     \\  \implies { \bold{(y - 4) = 2(x -  2)}} \\

     \\  \implies { \bold{y - 4 = 2x -  4}} \\

     \\  \implies { \boxed{ \bold{y  = 2x }}} \\

    • But point c(-1 , k) passing from the line . So that –

     \\  \implies { \bold{k  = 2( - 1) }} \\

     \\  \implies {  \boxed { \bold{k  =  - 2 }}} \\

    Hence , The value of k = -2

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