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The line represented by equation y=x is the perpendicular

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The line represented by equation y=x is the perpendicular [#permalink] New post 27 Oct 2012, 19:28
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The line represented by equation y=x is the perpendicular bisector of line segment AB. If A has the coordinates (-3,3), what are the coordinates of B?

[Reveal] Spoiler:
Hello Friends,

I would like you to help me with coordinate geometry. This is a problem from MGMAT.


I understand that the perpendicular bisector slope is 1 so the slope os segment AB is −1. so by substituting the values we get b.
y=mx+b
3=-1(-3)+b
0=b
line containing segment AB is y=-x
For these two lines
y=x———(1)
y=-x———(2)
so x=-x
then how to proceed?
how can we determine x=0 and y=0 and find midpoints.

The answer is B(3,-3)
Can you put some light?
Please explain step by step as my maths is pretty weak.
Thank you

Last edited by Bunuel on 29 Oct 2012, 05:51, edited 1 time in total.
Renamed the topic, edited the question and moved to PS forum.
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Re: coordinate geometry [#permalink] New post 27 Oct 2012, 22:24
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pranav123 wrote:
Hello Friends,
I would like you to help me with coordinate geometry. This is a problem from MGMAT. The line is represented by equation y = x is the perpendicular bisector of line segment AB. If AB has the coordinates (-3,3), what are the coordinates of B?

I understand that the perpendicular bisector slope is 1 so the slope os segment AB is −1. so by substituting the values we get b.
y=mx+b
3=-1(-3)+b
0=b
line containing segment AB is y=-x
For these two lines
y=x———(1)
y=-x———(2)
so x=-x
then how to proceed?
how can we determine x=0 and y=0 and find midpoints.

The answer is B(3,-3)
Can you put some light?
Please explain step by step as my maths is pretty weak.
Thank you


From the equations, you can see that the line y=-x is bisected at the origin by y = x. So the midpoint of segment AB is (0,0).

Midpoint of a line segment having points A(x_1,y_1) and B(x_2,y_2) is (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

We have the values of the point A and the midpoint. So point be can be easily found.

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Re: The line represented by equation y=x is the perpendicular [#permalink] New post 29 Oct 2012, 05:54
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Expert's post
pranav123 wrote:
The line represented by equation y=x is the perpendicular bisector of line segment AB. If A has the coordinates (-3,3), what are the coordinates of B?

[Reveal] Spoiler:
Hello Friends,

I would like you to help me with coordinate geometry. This is a problem from MGMAT.


I understand that the perpendicular bisector slope is 1 so the slope os segment AB is −1. so by substituting the values we get b.
y=mx+b
3=-1(-3)+b
0=b
line containing segment AB is y=-x
For these two lines
y=x———(1)
y=-x———(2)
so x=-x
then how to proceed?
how can we determine x=0 and y=0 and find midpoints.

The answer is B(3,-3)
Can you put some light?
Please explain step by step as my maths is pretty weak.
Thank you


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Re: The line represented by equation y=x is the perpendicular   [#permalink] 29 Oct 2012, 05:54
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