co-ordinate geometry

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francoisph: Master | Next Rank: 500 Posts; Posts: 124; Joined: Sun Mar 07, 2010 3:15 pm; Thanked: 1 times

by francoisph » Wed Jun 23, 2010 5:39 am

Question # 23
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) answer

could you explain clearly?please

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Source: Beat The GMAT — Problem Solving | Wed Jun 23, 2010 5:39 am

albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Wed Jun 23, 2010 5:48 am

Rewrite the line as y = 2x + 8

This is in slope intercept form and this tells us that the slope of our line is 2.

Now the perpendicular will therefore have a slope of -1/2

Start with E and use (y2 - y1) / (x2 - x1) = -1/2 so that the points (2,2) and the choices should validate this equation.

E. (-2,4) yields this very result and is hence our answer.

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ruplun: Master | Next Rank: 500 Posts; Posts: 232; Joined: Fri Jun 18, 2010 7:09 amFollowed by: 2 members; Thanked: 1 times

by ruplun » Wed Jun 23, 2010 8:34 am

Please can u explain , how the perpendicular slope is -1/2?

perpendicular will therefore have a slope of -1/2

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albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Wed Jun 23, 2010 8:37 am

ruplun wrote:Please can u explain , how the perpendicular slope is -1/2?

perpendicular will therefore have a slope of -1/2

Sure.

It is a property of perpendicular lines that the product of their slopes will always be equal to -1.

This can be derived using Pythagorean theorem, but just remember it for the GMAT

Other important slopes:

1. 2 parallel lines will always have the same slope.
2. A line parallel to the x-axis has a slope of zero.
3. A line parallel to the y-axis has an undefined slope.

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outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 amFollowed by: 3 members; Thanked: 46 times

by outreach » Wed Jun 23, 2010 10:24 am

Slope of line y - 2x - 8 = 0 is 2
Slope of perpendicular(m) = -1/2 and it passed through (2,2). substitute this in eq of line to find the equation of perpendicular

Eq of line y=mx+c
2=-(1/2)2+c
therefore c=3
hence eq of perpendicular
y=-(1/2)x+3 -(1)
another line eq y - 2x - 8 = 0 is given in the eq
y - 2x - 8 = 0
y=2x+8 -(2)

solve eq 1 and 2 to find value of x and y
E

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