Question

Read the following passage and answer the questions that follows: In a class room, four students Sita, Gita, Rita and Anita are sitting at A(3,4), B(6,7), C(9,4), D(6,1) respectively. Then a new student Anjali joins the class
(i) Teacher tells Anjali to sit in the middle of the four students. Find the coordinates of the position where she can sit.
(ii) Calculate the distance between Sita and Anita. (iii) Which two students are equidistant from Gita.

Answer 1

Coordinates of New Students Anjali  are (6 , 4) , Sita & Rita are equidistant from Gita

Step-by-step explanation:

A(3,4), B(6,7), C(9,4), D(6,1)

A & C are in same line

middle of A & C  is   (6 , 4)

B & D are in same line

middle of B & D is  also (6 , 4)

Hence

Anjali sits at  E (6 , 4)

EA = EB = EC = ED = 3

between Sita  (A) and Anita (D)

A(3,4)  &  D(6,1)

= √(6-3)² + (1-4)²

= 3√2

Sita (A) & Rita (C)  are equidistant from Gita  (B)

A(3,4) , B (6 , 7) = √(6-3)² + (7-4)² = 3√2

C(9,4),   B (6 , 7) = √(6-9)² + (7-4)² = 3√2

Answer 2

SOLUTION

GIVEN

Seeta ,Geeta ,Rita and Anita are sitting at A(3,4) B(6,7) C(9,4) D(6,1) respectively. A new student Anjali join the class

TO DETERMINE

(i) Teacher tells Anjali to sit in the middle of the four students. Find the coordinates of the position where she can sit.

(ii) Calculate the distance between Sita and Anita.

(iii) Which two students are equidistant from Gita.

EVALUATION

Here it is given that Seeta ,Geeta ,Rita and Anita are sitting at A(3,4) B(6,7) C(9,4) D(6,1) respectively.

Now a new student Anjali join the class

(i) Teacher tells Anjali to sit in the middle of the four students.

So the coordinates of the position where she can sit is the middle point of AC ( or BD )

Hence the coordinates of the position where she can sit

= Middle point of AC

$\displaystyle \sf{= \bigg( \frac{3 + 9}{2} \: , \: \frac{4 + 4}{2} \bigg) }$

$\displaystyle \sf{= \bigg( \frac{12}{2} \: , \: \frac{8}{2} \bigg) }$

$\displaystyle \sf{= ( 6 \: , \: 4 ) }$

(ii) The distance between Sita and Anita

= The distance between A & D

$\sf{ = \sqrt{ {(3 - 6)}^{2} + {(4 - 1)}^{2} \: \: } \: \: unit}$

$\sf{ = \sqrt{ {3}^{2} + {3}^{2} \: \: } \: \: unit}$

$\sf{ = \sqrt{9 + 9 \: \: } \: \: unit}$

$\sf{ = \sqrt{18 \: \: } \: \: unit}$

$\sf{ = 3\sqrt{2 } \: \: unit}$

(iii) The distance between A & B

$\sf{ = \sqrt{ {(3 - 6)}^{2} + {(4 - 7)}^{2} } \: \: unit}$

$\sf{ = \sqrt{ {3}^{2} + {3}^{2} } \: \: unit}$

$\sf{ = \sqrt{18} \: \: unit}$

$\sf{ =3 \sqrt{ 2 } \: \: unit}$

Distance between B & C

$\sf{ = \sqrt{ {(9 - 6)}^{2} + {(4 - 7)}^{2} } \: \: unit}$

$\sf{ = \sqrt{ {(3 )}^{2} + {(3)}^{2} } \: \: unit}$

$\sf{ =3 \sqrt{2 } \: \: unit}$

Distance between B & D

$\sf{ = \sqrt{ {(6- 6)}^{2} + {(1 - 7)}^{2} } \: \: unit}$

$\sf{ = \sqrt{ {(0)}^{2} + {(6)}^{2} } \: \: unit}$

$\sf{ = 6 \: \: unit}$

Hence A & C are equidistant from B

Hence Seeta and Rita is equidistant from Geeta

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