bmwhype2 wrote:

Is point A closer to point (1,2) than to point (2,1)?

1. Point A lies on the line y=x

2. Point A lies on the line y=-x

Is there an algebraic/formula approach to this

A should be it.

1. If point A lies on the line y=x, any point on this line has equal value for x and y and both are either positive or negative. Lets say point A lies on (4, 4).

i. The distance between A and (1, 2 ) = Sqrt {(4-1)^2 + (4-2)^2} = Sqrt {9 + 4 } = Sqrt (13)

ii. The distance between A and (2, 1 ) = Sqrt {(4-2)^2 + (4-1)^2} = Sqrt {4 + 9} = Sqrt (13)

Both are same.

If point A lies on (-3, -3).

i. The distance between A and (1, 2 ) = Sqrt {(-3-1)^2 + (-3-2)^2} = Sqrt (41)

ii. The distance between A and (2, 1 ) = Sqrt {(-3-2)^2 + (-3-1)^2} = Sqrt (41)

Both are equidistance. Suff..

2. If point A lies on the line y=-x, any point other than (0, 0) on this line has different values for x and y i.e. if x is +ve, y is -ve and vice versa. So any point on the line y = -x is not equidistance from point (1,2) and (2,1).

Lets say point A lies on (4, -4).

i. The distance between A and (1, 2 ) = Sqrt {(4-1)^2 + (-4-2)^2} = Sqrt {9 + 36 } = Sqrt (45)

ii. The distance between A and (2, 1 ) = Sqrt {(4-2)^2 + (-4-1)^2} = Sqrt {4 + 25} = Sqrt (29)

So these two points are not equidistance from A. NSF. Hence only A is correct.

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