Question

$\huge{\underline{\tt{Question:-}}}$
By using concept of equation of a line, prove that the three points (3,0)(-2,-2) are collinear.​

Answer 1

Answer:

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Line eqn of (3,0) and (-2,-2) is

y-o = 2/5 (x-3)

5y = 2x-6

2x-5y-6 = 0

put (8,2) in the equation

2(8)-5(2)-6 = 16-16 = 0

It satisfies the given equation so they are collinear points

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Answer 2

Correct Question :-----

• By using the concept of equation of a line, prove that the three points (3, 0),(– 2, – 2) and (8, 2) are collinear.

Concept used :------

→ The third point will satisfy the Equation of the line from the two points .

→ Equation of line from point (x1,x2) and (y1,y2) is given by,

y-y1 = [(y2-y1)/(x2-x1)]*(x-x1)

Solution :-------

here ,

(x1,y1) = (3,0) and (x2,y2) = (-2 , -2)

Putting values now in above formula we get,,

Equation of line =

→ (y-0) = (-2-0/-2-3)*(x-3)

→ y = 2/5 * (x-3)

→ 5y = 2x - 6

→ 2x - 5 y = 6

_________________________

Now, since all three points are collinear ,

So, putting third point (8,2) in line we get,

→ 2(8) - 5(2) = 6

→ 16 - 10 = 6

→ 6 = 6

Hence, Proved .....

So, all three points are collinear .....

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