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標題:

Intersection point

發問:

The coordinates of A and B are (-7, 2) and (3, -4) respectively. There is a line CD with a point P (1, 4) perpendicular to AB. AB intercepts CD. Find the distance between P and AB.

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最佳解答:

Slope of AB=(2+4)/(-7-3)= -3/5 ∴y-2= -3/5(x+7) 3x+5y+11=0....(1) is the equation of AB. ∵AD is perpendicular to CD, slope of CD × slope of AB= -1 ∴slope of CD= -1/(-3/5)=5/3 ∴y-4=5/3(x-1) 5x-3y-27=0.....(2) is the equation of CD. (1)x5/3-(2), 5x+(25/3)y+55/3-(5x-3y-27)=0 (34/3)y= -136/3 ∴y=-4.......(3) Putting (3) into (1), 3x+5(-4)+11=0,x=3 ∴The intercept point between AB and CD is (3,-4) ∴The distance required=√(3-1)^2+(-4-4)^2=2√17

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