Question

Find the value of 'a'for which the following points A (a,3) B (2,1 )and c (5 , a) are collinear hence find the equation of the line.....plz plz give the correct ans.......

Answer 1

Take these points equal to 0.and hence find the value of a by putting quadratic formula

Answer 2

Answer:

The value of a are 4,-1.

The equation of line is $a^2-3a-4=0$

Step-by-step explanation:

Given : Points A (a,3) B (2,1 )and c (5 , a) are collinear.

To find : The value of a and the equation of the line?

Solution :

Points A (a,3) B (2,1 )and c (5 , a) are collinear.

If the points are collinear the area of triangle is 0.

$(x_1,y_1)=(a,3) , (x_2,y_2)=(2,1) ,(x_3,y_3)=(5,a)$

$A=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

$0=\frac{1}{2}[a(1-a)+2(a-3)+5(3-1)]$

$0=[a-a^2+2a-6+10]$

$a^2-3a-4=0$

The equation of line is $a^2-3a-4=0$

Now, solving quadratic equation

$a^2-4a+a-4=0$

$a(a-4)+1(a-4)=0$

$(a-4)(a+1)=0$

$a=4,-1$

Therefore, The value of a are 4,-1.