InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Prove that the points (a, b),(a1,b1) and (a - a1, b - b1) are collinear if ab1 = a1b |
|
Answer» Consider the following points A(a,b), B(a1,b1), C(a−a1,b−b1) Since the given points are collinear, we have area(△ABC)=0 First find the area of area(△ABC) as follows: area(△ABC) = \(\frac{1}2\) |x1(y1−y3)+x1(y3−y1)+x3(y1−y1)| = \(\frac{1}2\) |a(b1−(b−b1))+a1((b−b1)−b)+(a−a1)(b−b1)| = \(\frac{1}2\) |a(b1−b+b1)+a1(b−b1−b)+a(b−b1)−a1(b−b1)| = \(\frac{1}2\) |−ab−a1b1+ab−ab1+a1b+a1b1| = \(\frac{1}2\) |−(ab1−a1b)| = (ab1−a1b) This gives, ab1−a1b=0 ∴ ab1 = a1b |
|