Question

Find the value of x for which the points (x,-1) (2,1) and (4,5) are collinear.

Answer 1

for the points to be collinear,
x1(y2-y3) + x2(y3-y1) + x3(y1-y2)=0... (1)
now the points are A(1,5) B(K,1) and C(4,11) i.e.
x1=1 y1=5
x2=K y2=1
x3=4 y3=11
put these values in equation 1..
1(1-11) + K(11-5) + 4(5-1) =0
-10+ 6K +16 =0
6K+6=0.... 6K=-6
i.e. K=-1...
hope it helps you.. mark brain if u like

Answer 2

Let A(x,-1)
B(2,1)
C(4,5)
If ABC is collinear then ar(ABC)=0
area of triangle=1/2[x1(y2-y3) +x2(y3-y1) +x3(y1-y2)]
1/2[x(1-5)+2(5+1)+4(-1-1)]=0
x(-4)+2(6)+4(-2)=0
-4x+12-8=0
-4x+4=0
4=4x
x=1