Question

if the points are A(3,-4),B(4,5)and C(X,14) ARE COLLINEAR FIND VALUE OF X

Answer 1

EXPLANATION.

→ points are → A ( 3,-4) B ( 4,5) and C (x, 14)

are collinear.

→ To find value of x.

$\sf : \implies \: x_{1} = 3 \: \: and \: \: \: y_{1} = - 4 \\ \\ \sf : \implies \: \: x_{2} = 4 \: \: \: and \: \: \: y_{2} = 5 \\ \\ \sf : \implies \: \: x_{3} = x \: \: \: and \: \: \: y_{3} = 14$

$\sf : \implies \: \: area \: of \: \triangle = \dfrac{1}{2} ( x_{1}( y_{2} - y_{3}) + x_{2}( y_{3} - y_{1}) + x_{3}( y_{1} - y_{2})) = 0\\ \\ \sf : \implies \: x_{1}( y_{2} - y_{3}) + x_{2}( y_{3} - y_{1}) + x_{3}( y_{1} - y_{2}) = 0$

→ 3 ( 5 - 14) + 4 ( 14 - (-4)) + x ( -4 - 5 ) = 0

→ 3 ( -9) + 4 ( 18) + x ( -9) = 0

→ -27 + 72 - 9x = 0

→ 45 - 9x = 0

→ x = 45/9

→ x = 5