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

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

Equation of a line passing through two points (1,2) and (2,1)

\(\frac{1-2}{2-1}=\frac{y-2}{x-1}\)

\(y = -x + 3\)

Slope =-1

1. y=x;
Slope = 1
Thus this line is perpendicular to the line (y = -x+3)

Not only this is perpendicular, but also it bisects the line in two equal parts.

Thus, all points on this line will be equidistant from both points (1,2) and (2,1).

Sufficient.

How to be sure that it is perpendicular bisector;

Let us find the midpoint of (1,2) and (2,1)

(2+1)/2, (1+2)/2

3/2, 3/2

Does this point satisfy the equation y=x; indeed it does.

2. y = -x

This line passes through the origin and goes at 45 degrees in 2nd and 4th quadrant.

So; if we visualize, when x=2, y=-2;
Point 2,1 will be closer

if x=-2, y=2
Point 1,2 will be closer.

Not sufficient.

Ans: "A"