Line rotated 90 degrees

[EbrahimHashem]

For the line whose equation is (y+2-b)/x=m +(2/x), m is not zero. If the line is rotated 90 degrees, then the slope of the line would be

(A) 1/m
(B) -1/m
(C) m
(D) -m
(E) m-2


HAVE FUN!

[Lock]

The answer should be B.
We have: y=mx+b. Now assuming that b=0 and m=2, we have y=2x. If we rotate this line 90 degrees, the equation of this new line will be y=(-1/2)*x. Here, the slope is (-1/m). Hence, B.

[neuroticA]

y+2-b/x=m+2/x

simplifying y=mx+b slope m

Now if the line is rotated 90 degrees it is perpendicular to the original line

so slope will be 1/m answer a

[finsisher]

D it is, for 2 lines to be perpendicular product of their slopes = -1 or m1*m2=-1 where m1 is slope of 1st line and m2 is slope of second line.
general form of equation is y = mx + C

[EbrahimHashem]

Try Try TRY! I'm not getting an affirmative answer! I have the official answer, but I'm not going to give it out as yet!

[finsisher]

sorry i miscalculated its B this says why I missed a 51 in GMAT

[EbrahimHashem]

Originally Posted by finsisher

sorry i miscalculated its B this says why I missed a 51 in GMAT

hummm if we have two perpendicular lines, their product should be -1, right? So, in this case, the first line has a slope of m and because the other line is perpendicular to it, its slope should be -1/m (m*-1/m=-1).

Note I'm still not giving you the official answer and I'm not telling you whether your explanation is right!

So, What if the two lines were parallel?

[clock60]

(y+2-b)/x=m+2/x
y+2-b=mx+2
y=mx+b
for the line to be rotated on 90 degree the slope should be negative and also
inverse i mean that multiply for example k*1/k=1
original slope is m
new one is -1/m
m*(-1/m)=-1
minus for the lines to be perpendicular

[mkx2000]

Well, the scalar product of orthogonal vectors is 0, so (B) it is.

(1,m)x(1,-1/m) = 0

If in doubt, just draw a chart for some value of m.

[Md. Minuddin]

Originally Posted by EbrahimHashem

For the line whose equation is (y+2-b)/x=m +(2/x), m is not zero. If the line is rotated 90 degrees, then the slope of the line would be

(A) 1/m
(B) -1/m
(C) m
(D) -m
(E) m-2


HAVE FUN!

If two line are perpendicular then the product of their slop is -1

here the equation is
(y+2-b)/x=m +(2/x)
Or,y+2-b=m x+2
Or, y=m x+b
Its slop is m


Let the slop of line perpendicular to it is m₁
So, mm₁=-1
Or,m₁=-1/m