Question

3) Check whether points (-5, 1), (1, 0) and (4,-2)
are collinear or not.
othermifits​

Answer 1

Answer:

not collinear(non - collinear)

Step-by-step explanation:

Given,

A = (-5 , 1)

B = (1 , 0)

C = (4 , - 2)

To Check :-

whether the points are collinear or not.

How To Do :-

To check those are collinear or not we need to apply the formula of area of the triangle. If the value of the area of triangle is '0' then the points are collinear. If the area of the triangle is not equal to '0' then the points are non - collinear.

Formula Required :-

Area of the triangle :-

$=|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

Solution :-

A = (-5 , 1)

Let,

x_1 = - 5 , y_1 = 1

B = (1 , 0)

Let,

x_2 = 1 , y_2 = 0

C = (4 , - 2)

Let,

x_3 = 4 , y_3 = - 2

Area of the triangle :-

$=|-5(0-(-2))+1(-2-1)+4(1-0)|$

$=|-5(0+2)+1(-3)+4(1)|$

$=|-5(2)-3+4|$

= |-10 -3+ 4|

= |-13 + 4|

= |-9|

= 9 sq.units

As the area of the triangle is ≠ 0 , So the points A , B , C are non - collinear points(not collinear).