Question 947058: what point on the line y=3x-1 is closest to the origin R^2 (0,0)? what is the distance from this point to the origin?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! what point on the line y=3x-1 is closest to the origin R^2 (0,0)? what is the distance from this point to the origin
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y=3x-1
slope=3
from the point on the given line, draw a perpendicular line terminating at the origin
this perpendicular line has a slope=-1/3(negative reciprocal)
its equation: y=-x/3
equate given line and perpendicular line:
3x-1=-x/3
9x-3=-x
10x=3
x=3/10=0.3
y=-x/3=-0.3/3=-0.1
point on the given line: (0.3,-0.1)
distance from point to origin: √(.3^2+.1^2)=√.09+.01=√.10≈.316
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