Question

Determine if the point (2,3) (4,0) and (6,-3)
are collinear
​

Answer 1

Solution:-

let ,

$\rm \: A(2,3) \: ,B(4,0) \: \: and \: \: C(6, - 3) \: are \: given \: point$

Then

$\rm (x_1 = 2,y_1 = 3), \rm(x_2 = 4,y_2 = 0) \: and \rm(x_3 = 6,y_3 = - 3)$

using the formula we get

$\rm \: x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)$

put the value on formula

$\rm \: 2(0 - ( - 3)) + 4( - 3 - 3) + 6(3 - 0)$

$\rm \: 2(3) + 4( - 6) + 6(3)$

$\rm \: 6 - 24 + 18$

$\rm \: 24 - 24$

$\rm \: \to \: 0$

Hence, the given points are collinear

Information about collinear

● slopes of any two pairs out of three pairs of points are same, this proves that A, B and C are collinear points.

●Area of triangle to find if three points are collinear.

●Three points are collinear if the value of area of triangle formed by the three points is zero.

●Apply the coordinates of the given three points in the area of triangle formula. If the result for area is zero, then the given points are said to be collinear.

●First of all, recall the formula for area of a triangle formed by three points.