Question

10th std .......state board maharashtra​

Answer 1

Question :

Q. How to use distance formula to identify the lines are Collinear or not ?

AnsWer :

• When three or more point lies on the same line and stay at straight line, it said to be Collinear.
• Non - Collinear When Any three or more point not lies on the same / straight line, it said to be Non- Collinear point.

Let Some Example :

We have,

• A , B and C Points.
• A( 0 , 0 )
• B( 2 , 0 )
• C( 5 , 0 )

We have distance Formula, Apply.

$\tt \dagger \: \: \: \: \: d = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 -y_1) }^{2} }$

$\rule{90}1$

• Distance AB.

$\tt \mapsto AB = \sqrt{ {(2 - 0)}^{2} + {(0 - 0)}^{2} }$

$\tt \mapsto AB = \sqrt{4}$

$\tt \mapsto AB =2 \: units.$

$\rule{90}1$

• Distance BC.

$\tt \mapsto BC = \sqrt{ {(5 - 2)}^{2} + {(0 - 0)}^{2} }$

$\tt \mapsto BC = \sqrt{9}$

$\tt \mapsto BC =3 \: units.$

$\rule{90}1$

• Distance AC.

$\tt\mapsto AC = \sqrt{ {(5 - 0)}^{2} + {(0 - 0)}^{2} }$

$\tt\mapsto AC = \sqrt{25}$

$\tt\mapsto AC =5 \: units.$

Note : Lines are Collinear than, AB + BC = AC.

$\rule{90}1$

A/Q,

$\tt \mapsto AB + BC = AC.$

$\tt \mapsto 2 + 3 = 5.$

$\tt \mapsto 5= 5.$

Answer 2

Answer:

* When three or more point lies on the same line and stay at straight line, it said to be Collinear.

* Non - Collinear When Any three or more point not lies on the same / straight line, it said to be Non- Collinear point.