Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
2.4k views
in Straight Lines by (26.9k points)
closed by

Show that the points \(\big(at\frac{2}{1},2at_1\big)\), \(\big(at\frac{2}{2},2at_2\big)\) and (a, 0) are collinear, if t1 t2 = – 1.

1 Answer

+1 vote
by (30.0k points)
selected by
 
Best answer

Let the given points be A(x1, y1) = \(\big(at\frac{2}{1}, 2at_1\big)\),

B(x2, y2) = \(\big(at\frac{2}{2}, 2at_2\big)\), and C(x3, y3) = (a, 0)

Area of ∆ABC

= \(\frac{1}{2}\)|x1 (y2 − y3) + x2 (y3 − y1) + x3 (y1 − y2)|

If t1t2 = – 1, then t1t2 + 1 = 0

Area of ∆ABC = 0

Hence, the given points are collinear.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...