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Question 1069290: Find coordinates for a point that is 5 units from the line 3x + 4y = 10.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find coordinates for a point that is 5 units from the line 3x + 4y = 10.
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Here's 1 way:
Find the slope of the line, = -3/4
Lines perpendicular has a slope that's the negative inverse, m = 4/3
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Pick a point on 3x + 4y = 10. (0,5/2) is as good as any.
Find the equation of a line thru (0,5/2) with slope = 4/3
y = (4/3)x + 5/2
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The difference in y-intercepts = 5/(cos(atan(m))
= 5/0.6 = 25/3
--> (0,25/3) is 5 units away.
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There are 2 lines 5 units from the given line.
y = (4/3)x + 5/2 ± 25/3
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