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

3

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

coordinates of the position where she can sit.

1

(ii) Calculate the distance between Sita and Anita. 1

(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

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Answer 2

(i) The position of Anjali will be (6,4).

(ii) 3√2 units

(iii) Sita and Rita

Step-by-step explanation:

(i) If we plot the position points of Sita, Gita, Rita and Anita on the coordinate plane, then we can see that the Sita (3,4) and Rita (9,4) are placed parallel to the x-axis and the coordinates of their midpoint are (6,4).

Again, if we plot the position points of Sita, Gita, Rita and Anita on the coordinate plane, then we can see that the Gita (6,7) and Anita (6,1) are placed parallel to the y-axis and the coordinates of their midpoint are (6,4).

Therefore, the position of Anjali will be (6,4).

(ii) The distance between Sita (3,4) and Anita (6,1) will be

d = $\sqrt{(3 - 6)^{2} + (4 - 1)^{2}} = 3\sqrt{2}$ units.

(iii) The distance between Sita (3,4) and Gita (6,7) will be

$d_1 = \sqrt{(6 - 3)^{2} + (7 - 4)^{2}} = 3\sqrt{2}$ units.

Again, the distance between Rita (9,4) and Gita (6,7) will be

$d_2 = \sqrt{(9 - 6)^{2} + (7 - 4)^{2}} = 3\sqrt{2}$ units.

Therefore, Sita and Rita are equidistant from Gita. (Answer).