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# The line represented by equation y=x is the perpendicular

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Intern
Joined: 18 Oct 2012
Posts: 4
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Kudos [?]: 14 [0], given: 9

The line represented by equation y=x is the perpendicular [#permalink]

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27 Oct 2012, 20:28
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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.

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, 06:51, edited 1 time in total.
Renamed the topic, edited the question and moved to PS forum.
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Kudos [?]: 1485 [1] , given: 116

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27 Oct 2012, 23:24
1
KUDOS
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.

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.

Kudos Please... If my post helped.
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Re: The line represented by equation y=x is the perpendicular [#permalink]

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29 Oct 2012, 06:54
1
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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.

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, 06:54
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