SOLUTION: The equation of line passing through origin and perpendicular to line: 2x + y - 5 = 0 is ____? A. 2x + y + 5= 0 B. x - 2y + 5 = 0 C. x - 2y - 5 = 0 D. x + 2y + 5= 0 E. None

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Question 1185462: The equation of line passing through origin and perpendicular to line:
2x + y - 5 = 0 is ____?
A. 2x + y + 5= 0
B. x - 2y + 5 = 0
C. x - 2y - 5 = 0
D. x + 2y + 5= 0
E. None of these
[Note: If answer is option E, then find the exact answer]
Found 3 solutions by ankor@dixie-net.com, greenestamps, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
The equation of line passing through origin and perpendicular to line:
2x + y - 5 = 0 is ____?
Change to the slope/intercept form
y = -2x + 5
the slope is -2, find the slope of a perpendicular line, s1*s2 = -1
-2*s2 = - 1
s2 = +.5
The line goes thru origin, therefore intercept is 0
The equation, then: y = .5x
put it back in the original form, mult eq by 2 and rearrange
x - 2y = 0
:
Answer is E
:
Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!


(1) You know the answer is E without doing much work; none of the equations in answer choices A to D passes through the origin, because (x,y)=(0,0) is not a solution to any of them.

(2) The method shown by the other tutor for finding the equation of the prescribed line is a good basic algebraic approach. But when the given equation is in the given form, there is a faster, more sophisticated way to get the answer.

For a given line with equation ax+by=c (c any constant), any line perpendicular to it has an equation of the form bx-ay=d (d is some constant). Note this equation is obtained by switching the coefficients of x and y in the original equation and changing the sign of one of them.

So, with the given line having equation 2x+y-5=0, we know the equation of any line perpendicular to it has an equation of the form x-2y+c=0.

Then to find the constant c, we use the fact that the origin (0,0) is on the line we want, so (x,y)=(0,0) must satisfy the equation:

x(0)-2(0)+c=0
0+c=0
c=0

And the equation we want is

ANSWER: x-2y=0

Here is a graph showing the given line 2x+y-5=0 (red) and the line x-2y=0 (green) that is perpendicular to the given line and passing through the origin. Also shown are a couple of other lines with equations of the form x-2y=c for different constants c, showing that all those lines are perpendicular to the given line.
Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

The equation of line passing through origin and perpendicular to line:
2x + y - 5 = 0 is ____?
A. 2x + y + 5= 0
B. x - 2y + 5 = 0
C. x - 2y - 5 = 0
D. x + 2y + 5= 0
E. None of these
[Note: If answer is option E, then find the exact answer]
2x + y - 5 = 0 <===== Given equation

Switching coordinates on left side and then NEGATING the y-coefficient makes the left side of NEW equation: x - 2y

Substituting given point (0, 0) in order to get the right-side constant, then gives us: x - 2y = 0 - 0, and then:

x - 2y = 0 (CHOICE E.) 

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