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# Which point is symmetric with point (-5,-2) about the line

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Intern
Joined: 23 Dec 2005
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Which point is symmetric with point (-5,-2) about the line [#permalink]  28 Mar 2006, 07:18
Which point is symmetric with point (-5,-2) about the line represented by y=x?

How to approach problems like this ?
Manager
Joined: 21 Mar 2006
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I would say draw a graph y=x is a simple diagonal line. What point would be symmetric to (-5, -2). It obviously has to be a point that is the same for x as for y...

I am assuming that it is asking how it is symmetric to the line so then i would say the answer is (5,2) because it is symmetric to the y=x line on the opposite side. draw it out i think it might help
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A.P.

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Joined: 24 Sep 2005
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Ethan wrote:
Which point is symmetric with point (-5,-2) about the line represented by y=x?

How to approach problems like this ?

let the symmetric point be (a,b)
We have the midpoint of (a,b) and ( -5,-2) be on the line y=x
---> 1/2( -5+a) = 1/2 ( -2+b) --> a-b= 3 (1)

We also have the slope of the line connecting (-5,-2) and (a,b) be -1 ( since this line is perpendicular to the line y=x)
--> (-2-b)/ (-5- a) = -1 ---> -2-b= 5+ a --> a+b= -7 (2)

Solving (1) and (2) , get a= -2, b= -5
--> the sym point is (-2,-5)
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