Math, asked by Sunny5095, 5 months ago

If the points (p1,q1),(p2,q2)and (p1-p2,q1-q2) are collinear , then prove that p1q2=p2q1.

Answers

Answered by devindersaroha43
0

Answer:

Step-by-step explanation:

Given:

p  

1

​  

x+q  

1

​  

y=1,p  

2

​  

x+q  

2

​  

y=1 and p  

3

​  

x+q  

3

​  

y=1

The lines will be concurrent if

​  

 

p  

1

​  

 

p  

2

​  

 

p  

3

​  

 

​  

 

q  

1

​  

 

q  

2

​  

 

q  

3

​  

 

​  

 

−1

−1

−1

​  

 

​  

=0

Or  

2

1

​  

 

​  

 

p  

1

​  

 

p  

2

​  

 

p  

3

​  

 

​  

 

q  

1

​  

 

q  

2

​  

 

q  

3

​  

 

​  

 

1

1

1

​  

 

​  

=0

Or  

△=0

i.e., area of a triangle formed by the points (p  

1

​  

,q  

1

​  

), (p  

2

​  

,q  

2

​  

), and (p  

3

​  

,q  

3

​  

) is zero and as such the points are collinear.

Similar questions