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06 Mar 2012, 10:37
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:36) correct
32%
(02:38)
wrong
based on 211
sessions
History
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In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3
Can anybody help me with this problem?! I really have no idea how to attack this problem..
Thanks!!
A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3
Can anybody help me with this problem?! I really have no idea how to attack this problem..
Thanks!!
06 Mar 2012, 12:01
Kudos
Bookmarks
In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3
The equation of line m is y=-4x+k. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A.
For more on this subject check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html
Hope it helps.
A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3
The equation of line m is y=-4x+k. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A.
For more on this subject check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html
Hope it helps.
General Discussion
06 Mar 2012, 11:46
Kudos
Bookmarks
This is an interesting problem, and I haven't solved it either as I am still learning this stuff. so far I've gotten about 3 different wrong answers.
I re wrote the equation of the line M: to Y=-4x + k
Given that N is perpendicular I believe the slope should be the opposite of M's, and it says it passes through the origin so I believe its intercept is 0 so i re wrote line N: to Y=4x + 0
the only point where these two lines share is there intersection where line M=N
-4x+k = 4x+0
k = 8x
x= k/8
plug into either equation to solve for Y = K/2
intersection point is K/8, K/2
since this is equal to P, k/8= R and K/2 = r+1
I think I must have made a mistake because after this point I get various answers that are wrong.
K/8 = K/2 + 1
I solve for K = - 8/3
then I plug back in to solve for R given R= k/8 thus
-8/3 divided by 8
and I get -1/3 = r
an exact difference of positive one... what did i do wrong?
I re wrote the equation of the line M: to Y=-4x + k
Given that N is perpendicular I believe the slope should be the opposite of M's, and it says it passes through the origin so I believe its intercept is 0 so i re wrote line N: to Y=4x + 0
the only point where these two lines share is there intersection where line M=N
-4x+k = 4x+0
k = 8x
x= k/8
plug into either equation to solve for Y = K/2
intersection point is K/8, K/2
since this is equal to P, k/8= R and K/2 = r+1
I think I must have made a mistake because after this point I get various answers that are wrong.
K/8 = K/2 + 1
I solve for K = - 8/3
then I plug back in to solve for R given R= k/8 thus
-8/3 divided by 8
and I get -1/3 = r
an exact difference of positive one... what did i do wrong?
