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# Co-rodinate Geometry

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Manager
Joined: 11 Apr 2009
Posts: 157

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07 May 2009, 15:25
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

The co-ordinates of the foot of the perpendicular from the point (2, 2) on the line y – 2x – 8 = 0 are

(A) (–1, 6)

(B) (–1, –4)

(C) (–2, 10)

(D) (2, 4)

(E) (–2, 4)

Can anyone give a detailed explaination and source of other such problems? Thanks
Senior Manager
Joined: 08 Jan 2009
Posts: 317

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08 May 2009, 00:20
Let L1 = y -2x -8 = 0 -----------1

You need to find the eqn of the perpendicular line (L2).

slope of L1 = 2. Slope of L2 = -1/2 . ( property for perpendicular line m1 * m2 = -1 )

The eqn of L2 is y = mx + c therefore y = -1/2 * x + c .

This line passes through (2,2) therefor c = 3 the L2 = y = 1/2 x + 3 ----------2

solve both the eqn u will get x= -2 and y = 4

Ans . E
Manager
Joined: 12 Apr 2006
Posts: 210
Location: India

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19 May 2009, 04:56
It's E. I solved this way

Slope of given equation y = 2x + 8 is 2, and the line | to this will have slope of -1/2

Slope of perpendicular line with coordinates (2, 2) and (-2, 4) = 4-2/-2-2 = -1/2. Hence E is the answer
Manager
Joined: 11 Apr 2009
Posts: 157

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20 May 2009, 05:52
Thanks for the shorter way of solving this equation Humans. Appreciate it.
Re: Co-rodinate Geometry   [#permalink] 20 May 2009, 05:52
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