SOLUTION: Find the distance from point (6,8) to the line 2x+5y=7

Question 210746: Find the distance from point (6,8) to the line 2x+5y=7

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the distance from point (6,8) to the line 2x+5y=7
2x+5y=7 --> y = (-2/5)x + 7/5
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The shortest line between the 2 will be perpendicular to the given line.
The slope, m, of 2x+5y= 7 is -2/5.
The slope of lines perpendicular will be the negative inverse, +5/2.
Use y-y1 = m*(x-x1) to find the eqn thru the point perpendicular to the given line.
y-8 = (5/2)*(x-6)
y = (5/2)x -7 Line perpendicular
y = (-2/5)x + 7/5 Given line
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Solve for the intersection point:
Since they both equal y:
(5/2)x - 7 = (-2/5)x + 7/5
25x - 70 = -4x + 14
29x = 84
x = 84/29
Solve for y:
2x+5y = 7
168/29 + 5y = 203/29
5y = 35/29
y = 7/29
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Now find the distance from (6,8) to (84/29,7/29)

s =~ 8.3563 units

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