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

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 Click here to see ALL problems on Length-and-distance Question 210746: Find the distance from point (6,8) to the line 2x+5y=7 Answer by Alan3354(30993)   (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 --------- 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 ------------ 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 -------- Now find the distance from (6,8) to (84/29,7/29) s =~ 8.3563 units