quantskillsgmat wrote:square ABCD lie in first quadrant of xy plane.A(4,6),B(8,6), C(8,2) ,D(4,2). point p lie on x axis and its coordinate is (6,0). A certain computer programe randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is prob that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4

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Any line through point P that does NOT pass through the two shaded regions will NOT pass through the square.
Any line through point P that passes through one of the shaded regions must pass through the other.
The slope of line L = (2-0)/(4-6) = -1.
The slope of line M = (2-0)/(8-6) = 1.
Since the slopes are negative reciprocals, line L is perpendicular to line M.
The intersection of lines L and M forms four 90 degree angles.
The sum of these four angles is 360.
Thus, the fraction of the coordinate plane taken by the two shaded regions = 180/360 = 1/2.
Thus, the probability that a line through point P will NOT pass through the two shaded regions = 1-1/2 = 1/2.

The correct answer is C.

Fantastic explanation.. thanks so much..

GMATGuruNY wrote:

quantskillsgmat wrote:square ABCD lie in first quadrant of xy plane.A(4,6),B(8,6), C(8,2) ,D(4,2). point p lie on x axis and its coordinate is (6,0). A certain computer programe randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is prob that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4

DRAW the figure:
]

Any line through point P that does NOT pass through the two shaded regions will NOT pass through the square.
Any line through point P that passes through one of the shaded regions must pass through the other.
The slope of line L = (2-0)/(4-6) = -1.
The slope of line M = (2-0)/(8-6) = 1.
Since the slopes are negative reciprocals, line L is perpendicular to line M.
The intersection of lines L and M forms four 90 degree angles.
The sum of these four angles is 360.
Thus, the fraction of the coordinate plane taken by the two shaded regions = 180/360 = 1/2.
Thus, the probability that a line through point P will NOT pass through the two shaded regions = 1-1/2 = 1/2.

The correct answer is C.