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
1.6k views
in Straight Lines by (25 points)
edited by

Find the orthocenter of the triangle with the following vertices@ (- 2, - 1) , (6, - 1) and (2, 5); (5, - 2) , (- 1, 2) and (1, 4)

Please log in or register to answer this question.

1 Answer

+1 vote
by (31.3k points)

Equation of line BD is

\(y + 1 = \cfrac{-1}{\frac{5 + 1}{2 + 2}}(x - 6)\)

(∵ slope of line BD \(=\frac{-1}{\text{slope of line AC}}\))

y + 1 = -4/6 (x - 6)

y + 1 = -2/3 (x - 6)

\(\Rightarrow\) 3y + 3 = -2x + 12

\(\Rightarrow\) 2x + 3y = 9 .....(1)

Now, equation of line AF is

\(y + 1 = \cfrac{-1}{\frac{5 + 1}{2 - 6}}(x + 2)\) (slope of line AF \(=\frac{-1}{\text{slope of line BC}}\))

\(\Rightarrow\) y + 1 = 4/6 (x + 2)

\(\Rightarrow\) 3y + 3 = 2x + 4

\(\Rightarrow\) -2x + 3y = 1 ....(2)

Adding equation (1) and (2), we get

6y = 10

\(\Rightarrow\) y = 10/6 = 5/3

By putting y = 5/3 in equation (1), we get

2x = 9 - 5 = 4

\(\Rightarrow\) x = 4/2 = 2

Hence, orthocenter of the triangle is (2, 5/3).

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

...