Question 258389
Determine the shortest distance from (9,5) to 5x + 3y =15
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The shortest distance is a perpendicular distance.
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Find the slope of the given line:
y = (-5/3)x + 5
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ANY line perpendicular to that line must 
have a slope = 3/5
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Find the equation of the line with slope = 3/5 and passing thru (9,5):
5 = (3/5)9 + b
5 = (27/5) + b
b = (25/5)-(27/5)
b = -2/5
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Equation you want: y = (3/5)x - (2/5)
5y = 3x - 2
3x - 5y = 2
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Find the point of intersection of the two equations:
3x-5y = 2
5x+3y = 15
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Multiply 1st Eq. by 3; Multiply 2nd equation by 5:
9x - 15y = 6
25x- 15y = 75
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Add and solve for "x":
34x = 81
x = 81/34
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Substitute to solve for "y":
3(81/34) - 5y = 6
243/34 - 5y = 6
5y = (243-204)/34
5y = 39/34
y = (39/170)
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The point of intersection is (81/34 , 39/170)
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Find the distance between that point and (9,5)
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Cheers,
Stan H.