Straight Line and Pair of Straight Lines 3 Question 11

12. Using coordinate geometry, prove that the three altitudes of any triangle are concurrent.

(1998, 8M)

Show Answer

Answer:

Correct Answer: 12. x+5y=±52

Solution:

  1. Let the vertices of a triangle be, O(0,0)A(a,0) and B(b,c) equation of altitude BD is x=b.

Slope of OB is cb.

Slope of AF is bc.

Now, the equation of altitude AF is

y0=bc(xa)

Suppose, BD and OE intersect at P.

Coordinates of P are b,b(ab)c

Let m1 be the slope of OP=abc

and m2 be the slope of AB=cba

Now, m1m2=abccba=1

We get, that the line through O and P is perpendicular to AB.



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक