Question

if point A(1,2) , B (0,0) , and C (a,b) are collinear then find the relationship between a and b​

Answer 1

${\huge\mathfrak\color{Red}{Answer~is~b+2a=0 }}$

We know that,

collinear points made triangle of area 0 unit^2

$area \: of \: triangle \: = \sqrt{1(0 - b) + 0(b - 2) + a(2 - 0)} \\ \\ 0 = \sqrt{b + 0 + 2a} \\ \\ \sqrt{b + 2a } = 0 \\ \\ b + 2a = 0$

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Answer 2

Answer:

Let be co-ordinator of A = (1,2)

Co-ordinator of B=(0,0)

Co-ordinator of C= (a,b)

area of (∆ABC)=0

1/2[x1(y2-y3)+x²(y3-y1)+x3(y1-y2)]=0

1/2[1(0-b)+0(b-1)+a(2+0)]=0

[-b+0+2a]=0

b+2a=0

2a+b=0