Question

Show that the points (a,1) , (b,1) , (c,1) are collinear points.

Answer 1

GIVEN :

The points are (a,1) , (b,1) , (c,1)

TO FIND :

The given points  (a,1) , (b,1) , (c,1) are collinear

SOLUTION :

Given  points are (a,1) , (b,1) , (c,1)

Let the points (a,1) , (b,1) , (c,1) be $(x_1,y_1)$ ,$(x_2,y_2)$ ,$(x_3,y_3)$ respectively.

Here, $x_1 = a$, $x_2 = b$, $x_3 = c$, $y_1 = 1$, $y_2 = 1$, $y_3 = 1$.

We know that if the points are collinear then area(∆ABC) = 0.

$Area=\frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$

Substitute the values in the formula we get,

$A= (\frac{1}{2})|a(1 - 1) + b(1 - 1) + c(1 - 1)|$

$=\frac{1}{2}|0+0+0|$

$=\frac{1}{2}(0)$                 

∴ Area = 0

∴ the given points (a,1) , (b,1) , (c,1) are collinear.

Answer 2

Answer:

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