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Question 317624: Find the point on the line y = 2x - 5 that is nearest the origin.
a. (2 , -1)
b. (1 , 2)
c. (2 , 2)
d. (-1 , 1)
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the point on the line y = 2x - 5 that is nearest the origin.
a. (2 , -1)
b. (1 , 2)
c. (2 , 2)
d. (-1 , 1)
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The shortest distance from the origin to the line is perpendicular to the line.
The slope of y = 2x - 5 is 2.
The slope of lines perpendicular have a slope that's the negative inverse,
m = -1/2.
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Use y = mx + b and the point (0,0) --> y = (-1/2)x
Find where y = -x/2 intersects y = 2x - 5
-x/2 = 2x - 5
-x = 4x - 10
-5x = -10
x = 2
y = -1
--> the point (2,-1) nearest the origin
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Tho is wasn't asked for:
The distance from the origin is
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