# SOLUTION: find the distance from (6,5) to the line defined by y=-2x-8. express as radical or a number rounded to the nearest hundredth

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 Geometry: Length, distance, coordinates, metric length Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Length-and-distance Question 178259: find the distance from (6,5) to the line defined by y=-2x-8. express as radical or a number rounded to the nearest hundredthAnswer by Alan3354(31530)   (Show Source): You can put this solution on YOUR website!find the distance from (6,5) to the line defined by y=-2x-8. express as radical or a number rounded to the nearest hundredth ------------------------- Find the eqn of the line thru (6,5) perpendicular to y=-2x-8. All lines perpendicular to it have a slope, m, that's the inverse negative. y = -2x - 8 is in slope-intercept form, and its slope is -2, so we will find a line thru (6,5) with a slope of +1/2. y - y1 = m*(x - x1) where (x1,y1) is (6,5) y - 5 = (1/2)*(x - 6) 2y - 10 = x - 6 2y = x + 4 ---------------- Solve the pair of eqns by subbing y into 2y = x + 4 2y = x + 4 2*(-2x-8) = x+4 -4x-16 = x+4 5x = -20 x = -4 ------------- y = -2x-8 = -2*(-4)-8 y = 0 The lines intersect at (-4,0) ----------------- Now find the distance from (6,5) to (-4,0) s = sqrt((diff in y)^2 + (diff in x)^2) s = sqrt((0-5)^2 + (-4-6)^2) s = sqrt(25+100) = sqrt(125) distance =~11.2 units