##### 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, C and D? If so, what should be his position?

By observing the positions of the students as given in the figure we can say that, A, B, C and D are forming a quadrilateral. So the vertices of this quadrilateral will be A (3, 5), B (7, 9), C (11, 5) and D (7, 1).

Now,

To find out the type of this quadrilateral we have to find all its sides;

By distance formula;

D =

So,

AB =

AB =

AB

BC =

CD =

And DA =

We see that, AB = BC = CD = DA i.e., all sides are equal.

Now, we find length of both diagonals;

AC =

= 8

And BD =

= 8

Here, AC = BD

Since AB = BC = CD = DA and AC = BD

So we can say that ABCD is a square. As we also know that diagonals of a square bisect each other. So, P be position of Jaspal in which he is equidistant from each of the four students A, B, C and D

Calculate the coordinates of point P;

Coordinates of P = Mid - point of AC

= = (7, 5)

Since, mid - point of a line segment having points (x1, y1) and (x2, y2) is

Hence, the required position of Jaspal is (7, 5).

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