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coordinate geometry

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by rahul.s » Tue Feb 09, 2010 8:26 pm
the line represented by the equation x = y is the perpendicular bisector of the line segment AB. if A has the coordinates (-3, 3), what are the coordinates of B?

[spoiler]OA is (3, -3)[/spoiler]
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by kvamsy » Tue Feb 09, 2010 9:14 pm
rahul.s wrote:the line represented by the equation x = y is the perpendicular bisector of the line segment AB. if A has the coordinates (-3, 3), what are the coordinates of B?

[spoiler]OA is (3, -3)[/spoiler]
If we have options, We can track very easily by using the formula Slope= (Y2-Y1)/(X2-X1) should be equal to -1 (for a Perpendicular bisector).

Hope this helps
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by papgust » Tue Feb 09, 2010 9:27 pm
Equation of a line x=y is a perpendicular bisector of AB.

Slope of eqn (x=y) = 1

Since its perpendicular to AB, slope of AB is -1 (m1 * m2 = -1 if lines are perpendicular)

As slope of AB is -1, it DEFINITELY passes through 2nd and 4th quadrant. One of the points is (-3, 3) which lies in 2nd quadrant. So, the other end lies in the 4th quadrant. Answer can be (3, -3) --> which lies in 4th quadrant

[If you provide the answer choices, the answer can be chosen much easily]
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by rahul.s » Tue Feb 09, 2010 9:29 pm
papgust wrote:[If you provide the answer choices, the answer can be chosen much easily]
i would've, but this problem is from the mgmat book, which doesn't contain any answer options.
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by ajith » Thu Feb 11, 2010 9:14 am
rahul.s wrote:the line represented by the equation x = y is the perpendicular bisector of the line segment AB. if A has the coordinates (-3, 3), what are the coordinates of B?

[spoiler]OA is (3, -3)[/spoiler]
any line perpendicular to y =mx+c can be represented as y = -1/m (x)+ d
in this case m = 1

The equation of a line perpendicular to y=x is y = -x+d
now 3,-3 is a point on y = -x+d, => -3 = -3 +d => d = 0

y=x and y = -x intersect at (0,0)

Since B is a point on the line y = -x we can assume that (m , -m) is the co-ordinates of B

AO = BO

sqrt(3^2+3^2 )= 2m2
m = +/-3
m is not 3 ( if m =3 then 3,-3 becomes B and A&B coincide) so, m is -3
B is (m , -m) ; (-3,3)
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by shashank.ism » Thu Feb 11, 2010 10:10 am
rahul.s wrote:the line represented by the equation x = y is the perpendicular bisector of the line segment AB. if A has the coordinates (-3, 3), what are the coordinates of B?

[spoiler]OA is (3, -3)[/spoiler]
slope of line represented by x=y is m=1
so slope of line perpendicular to x=y =-1/m = -1 =m'
Hence equation of line AB is y=m'x + c --> y=-x+c
since (-3,3) lies on y=-x+c --> 3= - (-3) +c --> c=0
so equation of line AB: y= -x
now for coordinates of point B, point B lies on line AB . Thus there can be a lots of points on line AB
so we take a term n to identify point on line y=-x
hence B = (n,-n) where n belongs to real number and n is not equal to -3.(as (-3,3) represents A)
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