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