In a xy-plane, the line y=x is the perpendicular bisector of segment A

Question

In a xy-plane, the line y=x is the perpendicular bisector of segment AB. If the coordinates of A is (1,-2), what are the coordinates of B?

A. (-1, 2)
B. (-2, 1)
C. (-2, -1)
D. (-3, 2)
E. (-4, 3)

gmatophobia · Answer

As the x = y is the perpendicular bisector, the point B will me a mirror image of point A over the origin. Hence point B = (-2,1).

Option B

Himanshiog · Answer

The mirror image is option 1 no? Please explain

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gmatophobia · Answer

The reflection is over origin.

(a,b) when reflected over origin becomes (b, a)

sk1999 · Answer

Can somebody please explain using another method?

Kinshook · Answer

In a xy-plane, the line y=x is the perpendicular bisector of segment AB.

If the coordinates of A is (1,-2), what are the coordinates of B?

Let the coordinates of B be (x,y)

Slope of AB = (y+2)/(x-1) 
Since AB is perpendicular to the line y=x

Slope of AB * Slope of (y=x) = -1
(y+2)/(x-1) * 1 = -1
y+2 + x - 1 = 0; x <>1
x + y + 1 = 0; 
y = -(x+1)

Perpendicular distance from Point B (1,-2) to the line (x-y= 0) =  |1+2|/\sqrt{2} = 3/\sqrt{2}

Perpendicular distance from Point A (x,y) to the line (x-y= 0) =  (1+2)/\sqrt{2} = 3/\sqrt{2}  =  x-y/\sqrt{2}

Since perpendicular distance from Point B (1,-2) to the line (x-y= 0) = Perpendicular distance from Point A (x,y) to the line (x-y= 0)

3/\sqrt{2} = |x-y|/\sqrt{2} 
|x-y| = 3
x+y=-1

Case 1: x -y =3; x+y=-1; x = 1; y=-2; Since coordinates of point A is different from that of point B; Not possible
Case 2: y-x = 3; x+y=-1; y = 1;x = -2; Coordinates of point A = (-2,1)

IMO B

In a xy-plane, the line y=x is the perpendicular bisector of segment A

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GMAT Problem Solving (PS) Questions

In a xy-plane, the line y=x is the perpendicular bisector of segment A

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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