Question

if the points (x,y) , (2,3) and (-3,4) are collinear then

Answer 1

Answer:

(x+5y) = 17

Step-by-step explanation:

  1/2[ x(3-4) + 2(4-y) -3(y-3)] = 0

or,          3x-4x+8-2y-3y+9    = 0

or,           -x+17-5y                  = 0

or,             -(x+5y)                   = -17

or,               (x+5y)                   = 17

Answer 2

Given:

• (x , y), (2 , 3) and (-3 ,4) are Collinear

Solution

If Points are Collinear then,

$\\ {\tt{ (x_1y_2 + x_2y_3 + x_3y_1) - ( y_1x_2 + y_2x_3 + y_3x_1) = 0 }} \\ \\ \\ \colon\implies{\tt{ (x \times 3 + 2 \times 4 +(-3) \times y) - (y \times 2 + 3 \times (-3) + 4 \times x) = 0 }} \\ \\ \\ \colon\implies{\tt{ (3x + 8 - 3y)-(2y-9+4x) = 0 }} \\ \\ \\ \colon\implies{\tt{ 3x + 8 - 3y - 2y + 9 - 4x = 0 }} \\ \\ {\tt{ Multipling \ both \ side \ with \ (-) }} \\ \\ \\ \colon\implies{\tt{ -(- x - 5y + 17) = -(0) }} \\ \\ \\ \colon\implies{\tt{ x + 5y - 17 = 0}} \\ \\ \\ \colon\implies{\boxed{\tt\pink{ x + 5y = 17 }}}$

Hence,

• If the points (x,y) , (2,3) and (-3,4) are collinear then ( x + 5y = 17 ).