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Given two points P = (3, 0) and Q = (0, 6), find the co-ordinates of

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Given two points P = (3, 0) and Q = (0, 6), find the co-ordinates of  [#permalink]

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New post 24 Nov 2019, 08:28
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Given two points P = (3, 0) and Q = (0, 6), find the co-ordinates of the point A, lying on the line x = - y, so that the triangle PAQ has the least possible perimeter.

(A) ( 1, -1 )
(B) ( -1, 1 )
(C) (-0.5,0.5)
(D) ( 2, -2)
(E) (0,0)
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Re: Given two points P = (3, 0) and Q = (0, 6), find the co-ordinates of  [#permalink]

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New post 01 Dec 2019, 02:44
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CaptainLevi wrote:
Given two points P = (3, 0) and Q = (0, 6), find the co-ordinates of the point A, lying on the line x = - y, so that the triangle PAQ has the least possible perimeter.

(A) ( 1, -1 )
(B) ( -1, 1 )
(C) (-0.5,0.5)
(D) ( 2, -2)
(E) (0,0)


for the ∆ PAQ to have least perimeter the distance of QA has to be minimum possible at when the point A is at origin (0,0)
IMO E
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Re: Given two points P = (3, 0) and Q = (0, 6), find the co-ordinates of  [#permalink]

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New post 02 Dec 2019, 01:44
CaptainLevi wrote:
Given two points P = (3, 0) and Q = (0, 6), find the co-ordinates of the point A, lying on the line x = - y, so that the triangle PAQ has the least possible perimeter.

(A) ( 1, -1 )
(B) ( -1, 1 )
(C) (-0.5,0.5)
(D) ( 2, -2)
(E) (0,0)


As line Equation is X= -Y

Line will cross through (0,0), From Quandrant 2 & 4.

with Only Point (0,0), will give Perimeter of Triangle PAQ least. Else, for other points , it will increase.

IMO-E

:please Please give kudos, if You find my explanation good Enough :please
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Re: Given two points P = (3, 0) and Q = (0, 6), find the co-ordinates of  [#permalink]

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New post 05 Dec 2019, 02:52
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The shortest distance between skew lines is equal to the length of the perpendicular between the two lines.

The perpendicular of x=-y will be y=x (opposite bisector of the coordinate plane). Hence the least distance between PQ and line:x=-y will pass from A(0,0).

IMO E
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Re: Given two points P = (3, 0) and Q = (0, 6), find the co-ordinates of   [#permalink] 05 Dec 2019, 02:52
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Given two points P = (3, 0) and Q = (0, 6), find the co-ordinates of

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