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Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure.

Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, Cand D. If so, what should be his position?

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(7, 5)

(7, 1)

(5, 5)

(7, 7)

answer is A.

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Detailed Solution

It is given that,
From the graph,

A (3, 5), B (7, 9), C (11, 5) and D (7, 1)

.
On joining given points, we get,
Question Image

.
We know that,
The distance between any two points in a Cartesian plane

M a, b and N c, d

is given by

M N = (c − a) 2 + (d − b) 2

.
Then,

From above we see that all the four sides are equal.
Now,

A C = (11 − 3) 2 + (5 − 5) 2 = 64 = 8 And B D = (7 − 7) 2 + (1 − 9) 2 = 64 = 8

The diagonals are also equal.
Thus, we can say that

ABCD

is a square.
∴ Jaspal's position will be the midpoint

M (x, y)

between AC and BD.
Since, if the coordinates of two points are

x 1, y 1

and

x 2, y 2

then the coordinate of the middle point of the two points will be

x 1 + x 2 2, y 1 + y 2 2

.
Then,

(x, y) = 3 + 11 2, 5 + 5 2 = (7, 5)

The position of Jaspal is at

M (7, 5)

.
Hence, option (1) is correct.

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