B is a point equidistant from points A and C. How far is B from either

Equidistant means that distance between B to A or B to C is the same;
However, depending where B is positioned the distance can change!

(1) insufic

distance AC = √(1-2)^2+(2-1)^2 = √2

(2) insufic

distance AC = √(1-2)^2+(2-1)^2 = √2

(1/2) insufic

Ans (E)

Given that B is a point equidistant from points A and C. We are to determine AB=AC.

In order to determine AB=AC, we need the coordinates of A, B, and C, or we need the coordinates of A and C and an indication of the distance from the midpoint of AC to B.

Statement 1: The coordinates of the points A and C are (1,2) and (2,1), respectively
Statement 1 gives us the coordinates A and C without coordinate of B. We have no idea of the relationship between the midpoint of AC and point B, hence we are unable to determine the exact distance between AB=AC, which can be √((2-1)^2+(1-2)^2)/2 = (√2)/2, if C B is located at the midpoint of A and C or any number depending on the coordinate of B. Statement 1 is insufficient.

Statement 2: The distance between A and C is √2
Statement 2 is clearly insufficient. Knowing the distance between A and C, we only need to know the distance or relationship between the midpoint of A and C and point B. Since we are not privy to this information, statement 2 is insufficient.

1+2
still insufficient. The information provided in statement 2 can be gotten from statement 1. Hence, combining statements 1 and 2 does not provide any new useful information.

The answer is E.

B is a point equidistant from points A and C. How far is B from either point ?

(1) The coordinates of the points A and C are (1,2) and (2,1) ,respectively
(2) The distance between A and C is √2

So basically we can assume a circle with center B and two points on its circumference, A and B. we have to find out the radius of that circle, e.g distance of either between A and B or B and C.
1) We can calculate the distance between A and C. But for the radius, we need the point B. Not sufficient
2) Same info as 1. Not sufficient.
E is the answer.

1) The coordinates of the points A and C are (1,2) and (2,1) ,respectively...........without knowing the co ordinates of B we cannot find the distance of A/C from B ..............INSUFFICIENT
2) The distance between A and C is √2......INSUFFICIENT

Even after combining both without knowing the co ordinates of B we cannot find the distance of A/C from B.....INSUFFICIENT

OA:E

Statement 1: The coordinates of the points A and C are (1,2) and (2,1) ,respectively

There are infinite possibilities of points B which are equidistant from A and C hence

NOT SUFFICIENT


Statement 2: The distance between A and C is √2

There are infinite possibilities of points B which are equidistant from A and C and also infinite possibilities of A and C as well hence

NOT SUFFICIENT

Combining the statements

A and C are (1,2) and (2,1) which are at a distance of √2

But B still has infinite many possibilities hence

NOT SUFFICIENT

answer: Option E

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