Question

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

Answer 1

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.