SOLUTION: How far from the origin is the line 3x + 4y = 10?
(a) 1.5 units (b) 2 units (c) 2.5 units (d) 2.75 units
(e) None of the above
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Question 287623: How far from the origin is the line 3x + 4y = 10?
(a) 1.5 units (b) 2 units (c) 2.5 units (d) 2.75 units
(e) None of the above
Found 2 solutions by josmiceli, richwmiller:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Another way to ask this question is:
What is the perpendicular distance from
the origin to this line?
Any line perpendicular to this line will
have slope =
The line through origin with this slope is:
Now the question is: What is the point where this line
intersects the given line?
By substitution:
and, substituting:
The distance formula is:
the distance is (b) 2 units
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
plug in 0 for x and find y 4y=10 y=10/4=5/2=2.5
plug in 0 for y and find x 3x=10 x=10/3=3 1/3
on the y axis it is 2.5
but we need to find the distance from a point to a line.
the slope of our line is -3/4
so the slope of the line from the origin to the line must be perpendicular and so 4/3
y-0=4/3(x-0)
y=4x/3
4x=3y
4x-3y=0
3x+4y=10
They intersect at
x = 6/5, y = 8/5
the distance from the (0,0) to (6/5,8/5) is
d=sqrt(y-y)^2+(x-x)^2
d=sqrt((6/5)^2+(8/5)^2)
d=2
http://www.worsleyschool.net/science/files/linepoint/method1.html
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