Question

for what value of m, the points (4,3),(m,1) and (1,9) are collinear

Answer 1

Hi ,
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The area of the triangle formed by

the points A (x1 , y1) , B(x2 , y2) and

C(x3 , y3) is

1/2 | x1(y2-y3)+x2(y3-y1)+x3(y1-y2) |
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According to the problem given,

Let A(x1,y1) = ( 4 , 3 ) ,

B(x2, y2) = ( m , 1 ),

C( x3 , y3 ) = ( 1 , 9 )

If A , B and C points are collinear

Area of triangle ABC = 0

1/2| x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | = 0

|4(1-9)+m(9-3)+1(3-1)|=0

| 4(-8) + m × 6 + 1 × 2 | = 0

| -32 + 6m + 2 | = 0

| -30 + 6m | = 0

- 30 + 6m = 0

6m = 30

m = 30 / 6

m = 5

Therefore,

If m = 5 , then A , B and C points are

collinear.

I hope this helps you.

:)

Answer 2

Answer:

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