If the points ( p1,q1) , (p2 , q2 ) and (p1+p2 ,q1+ q2) are collinear , show that p1q1 = p2q2 . About the author Reagan
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. Reply
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.