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

Answer 1

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