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Question 178276: find the distance from (2,1) to the line defined by y=-2x-5. Express as a radical or a number rounded to the nearest hundredth
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! find the distance from (2,1) to the line defined by y=-2x-5. Express as a radical or a number rounded to the nearest hundredth
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Do it like this one.
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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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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
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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
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y = -2x-8 = -2*(-4)-8
y = 0
The lines intersect at (-4,0)
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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
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