Math, asked by pulakalasanjana, 10 months ago

find the values of A so that the points (1, 4) (2, 7)(3,a) are collinear. ​

Answers

Answered by Anonymous
25

Given points :

  • A ( 1 , 4 )
  • B ( 2 , 7 )
  • C ( 3 , a )

To Find :

  • Value of a if points are collinear

Solution :

To find value of a. we use the formula

 \boxed{\sf \blue{ x_1(y_2 - y_3) + x_2(y_3 -y_1) + x_3( y_1 - y_2) = 0}} \\   \\ \sf Here \\ \\\sf x_1 = 1 \\ \\\sf x_2= 2 \\ \\\sf x_3= 3 \\\\\sf  y_1=4 \\\\ \sf y_2= 7 \\ \\\sf y_3 = a \\  \\ \implies \sf 1(7- a) + 2(a  - 4) + 3(4 - 7) = 0 \\  \\ \implies \sf 7 - a + 2a - 8 + 12 - 21 = 0 \\  \\ \implies \sf a  -  10 = 0 \\  \\ \large  \underline{ \boxed{  \green{ \sf a = 10}}}

If the value of a is 10 then the given points are collinear.

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