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ABCD is a parallelogram. M is the mid point of CD. The line BM is drawn intersecting AC at L and AD produced at E. Prove that EL=2BL

Geometry - Straight Lines & Triangle

Co-Ordinate Geometry

• Centroid : Medians are concurrent (G)
• Incentre: Int angle bisector are concurrent (I)
• Orthocentre : Altitudes are concurrent (H)
• Circumcentre : Perpendicular bisector are concurrent (O)
• H,G,O are collinearG divides HO in the ratio 2:1
• In an isoceles triangle all centres are collinear.

Problems:

1. Find the straight line passing through the point of intersection of straight lines x+y-5 = 0 and 4x-7y+10 = 0 and which is farthest from the point (2,2).
2. Prove that a Δ having all vertices with integer co-ordinates cannot be equilateral.??
   

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Solution: Download PDF

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IIT JEE EXAM 2011- EXAM DATE 10 April 2011, Last date to Apply = 15 December 2010

CO-ORDINATE WITH GEOMETRY

Geometry can be fun to learn and easy to score. But sometimes we take up the wrong approach, start solving unnecesssary equations and thus make the problem look all the more difficult and complex than it actually is. To get a better understanding of the topic, one must try solving the question by self rather than depending on the solution. The solution should help you get the right direction and not lessen your efforts and contribution.



Problem :
Determine the values of β if (0, β) lies inside the Δ formed by 2x + y + 2 = 0 , 3y -2x -5 = 0 and 4y +x = 14.


Try this problem yourself before checking out the solution. Click here to Download the solution 



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IIT JEE EXAM 2011- EXAM DATE 10 April 2011, Last date to Apply = 15 December 2010