You can put this solution on YOUR website! Find the exact directed distance from the line 4x+3y=5 to the point (2,-5).
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It's the distance from the point perpendicular to the line.
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Find the slope of the line
4x+3y=5
y = (-4/3)x + 5/3
Slope m = -4/3
The slope of lines perpendicular is the negative inverse = 3/4
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Find the eqn of the perpendicular line thru the point
Use y = mx + b and the point to find b
-5 = (3/4)*2 + b
b = -13/2
--> y = (3/4)x - 7/2 thru the point perpendicular to the given line
Find the intersection of the 2 lines by solving for x & y of the system
y = (3/4)x - 13/2
y = (-4/3)x + 5/3
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(-4/3)x + 5/3 = (3/4)x - 13/2
-16x + 20 = 9x - 78
x = 98/25
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y = -89/25
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Get the distance between the 2 points
d = 12/5 = 2.4 units
