Question

18. 8

7

6

5



4

3

2

1







Neena

Karan



Akash

Binu

Enter

A 1 2 3 4 5 6 7

Karan went to the Lab near to his home for COVID 19 test along with his family

members. The seats in the waiting area were as per the norms of distancing during this

pandemic (as shown in the above figure). His family member took their seats

surrounded by red circular area.

(i) Considering A as the origin, what are the coordinates of A?

a) (0,1) b) (1,0) c) (0,0) d)(-1,-1)

(ii) What is the distance between Neena and Karan ?

a) 10 b) 2√5 c)√10 d)√8

(iii) What are the coordinates of seat of Akash ?

a) (2,3) b) (3,2) c) (0,3) d) (2,0)

(iv) What will be the coordinates of a point exactly between Akash and Binu where a

person can be seated?

a) (3.5,2.5) b) (2.5,5) c) (10,5) d) (1.5,0.5)

(v) Determine the shape of the figure we get on joining the points where Karan’s family

members are seated.

a) Rectangle b ) Square c) Parallelogram d) Rhombus​

Answer 1

SOLUTION

TO DETERMINE

Karan went to the Lab near to his home for COVID 19 test along with his family members. The seats in the waiting area were as per the norms of distancing during this pandemic (as shown in the above figure). His family member took their seats surrounded by red circular area.

(i) Considering A as the origin, what are the coordinates of A?

a) (0,1) b) (1,0) c) (0,0) d)(-1,-1)

(ii) What is the distance between Neena and Karan ?

a) 10 b) 2√5 c)√10 d)√8

(iii) What are the coordinates of seat of Akash ?

a) (2,3) b) (3,2) c) (0,3) d) (2,0)

(iv) What will be the coordinates of a point exactly between Akash and Binu where a person can be seated?

a) (3.5,2.5) b) (2.5,5) c) (10,5) d) (1.5,0.5)

(v) Determine the shape of the figure we get on joining the points where Karan’s family members are seated.

a) Rectangle b ) Square c) Parallelogram d) Rhombus

EVALUATION

(i) Here A is origin

So the coordinates of A is (0,0)

Hence the correct option is c) (0,0)

(ii) In the figure :

Coordinates of Neena is (3,6)

Coordinates of Karan is (6,5)

∴ The distance between Neena and Karan

$\sf{ = \sqrt{ {(6 - 3)}^{2} + {(5 - 6)}^{2} } }$

$\sf{ = \sqrt{9 + 1} }$

$\sf{ = \sqrt{10} }$

Hence the correct option is c) √10

(iii) From the figure the coordinates of seat of Akash is (2,3)

Hence the correct option is a) (2,3)

(iv) The coordinates of seat of Akash is (2,3)

The coordinates of Binu is (5,2)

Midpoint of the line joining the points (2,3) & (5,2) is

$\displaystyle \sf{ = \bigg( \: \frac{2 + 5}{2} \: ,\: \frac{3 + 2}{2} \: \bigg)}$

$\displaystyle \sf{ = \bigg( \: \frac{7}{2} \: ,\: \frac{5}{2} \: \bigg)}$

$\displaystyle \sf{ = ( \: 3.5 \: ,\: 2.5 \: )}$

So the coordinates of a point exactly between Akash and Binu where a person can be seated is (3.5,2.5)

Hence the correct option is a) (3.5,2.5)

(v) From the figure we notice that each side is of length √10 unit and each angle is 90°

So that shape of the figure we get on joining the points where Karan’s family members are seated is Square

Hence the correct option is b) Square

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