Question

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? ​

Answer 1

The position of Jaspal is (7, 5).

Step-by-step explanation:

Let suppose A, B , C & D  are Stand  in drill  like Fig.

if we observe the position of  A, B , C & D  they re forming a quadrilateral. with the vertex A (3, 5), B (7, 9), C (11, 5) and D (7, 1).

As we know distance formula = $\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }$

So,

AB =  $\sqrt{(7 -3 )^{2}+(9 -5 )^{2}}$

AB =  $\sqrt{4^{2}+4^{2}}$

AB =  $\sqrt{16+16}$

AB = $\sqrt{32}$

BC = $\sqrt{(11 -7 )^{2}+(5 -9 )^{2}}$

BC = $\sqrt{4^{2}+(-4)^{2}}$

BC = $\sqrt{16+16}$

BC = $\sqrt{32}$

CD = $\sqrt{(7 -11 )^{2}+(1 -5 )^{2}}$

CD = $\sqrt{4^{2}+(-4)^{2}}$

CD = $\sqrt{16+16}$

CD = $\sqrt{32}$

DA = $\sqrt{(3 -7 )^{2}+(5 -1 )^{2}}$

DA = $\sqrt{(-4)^{2}+(4)^{2}}$

DA = $\sqrt{16+16}$

DA= $\sqrt{32}$

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

Now, find the diagonals,

AC =  $\sqrt{(11 -3 )^{2}+(5 -5)^{2}}$

AC = $\sqrt{(8)^{2}+(0)^{2}}$

AC = 8

BD = $\sqrt{(7 -7 )^{2}+(9 -1)^{2}}$

BD = $\sqrt{(0)^{2}+(-8)^{2}}$

BD = 8

here AC = BD

AB = BC = CD = DA and AC = BD

We can say that ABCD is a square

Let suppose the "P" is the position of jaspal

Now, find the co-ordinates of P

Coordinates of P = mid-point of AC

We know that mid-point formula =  $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

therefore coordinates of

P = $(\frac{3+11}{2},\frac{5+5}{2})$  =  $(\frac{14}{2},\frac{10}{2})$ = (7,5)

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

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Answer 2

Answer:

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 the figure. (a) What are the coordinates of A and B respectively? (i) A(3, 5); B(7, 8) (ii) A(5, 3); B(8, 7) (iii) A(3, 5); B(7, 9) (iv) A(5, 3); B(9, 7) (b) What are the coordinates of C and D respectively? (i) C(11, 5); D(7, 1) (ii) C(5, 11); D(1, 7) (iii) C(5, 11); D(7, 1) (iv) C(5, 11); D(-1, 7) (c) What is the distance between B and D? (i) 5 units (ii) 14 units (iii) 8 units (iv) 10 units (d) What is the distance between A and C? (i) 5 units (ii) 14 units (iii) 8 units (iv) 10 units (e) What are the coordinates of the point of intersection of AC and BD? (i) (7, 5) (ii) (5, 7) (iii) (7, 7) (iv) (5, 5)