Alia and Shagun are friends living on the same street in Patel Nagar. Shaguns house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point 0, i.e., the origin, Alia's house is at A. Shaguns house is at B and library is at C. Based on the above information, answer the following questions.

(i) How far is Alia's house from Shaguns house?

(ii) How far is the library from Shaguns house?

(iii) How far is the library from Alia's house?

(iv) Which of the following is true?

(v) How far is the school from Alia's house than Shaguns house?

Satellite image of a colony is shown below. In this view, a particular house is pointed out by a flag, which is situated at the point of intersection of x and y-axes. If we go 2 em east and 3 em north from the house, then we reach to a Grocery store. If we go 4 em west and 6 em south from the house, then we reach to a Electrician's shop. If we go 6 em east and 8 em south from the house, then we reach to a food cart. If we go 6 em west and 8 em north from the house, then we reach to a bus stand.

Based on the above information, answer the following questions.
(i) The distance between grocery store and food cart is

(ii) The distance of the bus stand from the house is

(iii) If the grocery store and electrician's shop lie on a line, the ratio of distance of house from grocery store to that from electrician's shop, is

(iv) The ratio of distances of house from bus stand to food cart is

(v) The coordinates of positions of bus stand, grocery store, food cart and electrician's shop form a

To raise social awareness about hazards of smoking, a school decided to start 'No smoking' campaign. 10 students are asked to prepare campaign banners in the shape of a triangle. The vertices of one of the triangle are P( -3,4), Q(3, 4) and R(-2, -1).

Based on the above information, answer the following questions.
(i) The coordinates of centroid of \(\Delta\)PQR are

(ii) If S be the mid-point of line joining P and Q, then coordinates of S are

(iii) If T be the mid-point of line joining Rand Q, then coordinates of T are

(iv) If Ube the mid-point of line joining Rand P, then coordinates of U are

(v) The coordinates of centroid of \(\Delta\)STU are

There are two routes to travel from source A to destination B by bus. First bus reaches at B via point C and second bus reaches from A to B directly. The position of A, Band C are represented in the following graph:

Based on the above information, answer the following questions.
(i) The distance between A and B is

(ii) The distance between A and Cis

(iii) If it is assumed that both buses have same speed, then by which bus do you want to travel from A to B?

(iv) If the fare for first bus is Rs10/km, then what will be the fare for total journey by that bus?

(v) If the fare for second bus is Rs 15/km, then what will be the fare to reach to the destination by this bus?

In an examination hall, students are seated at a distance of 2 m from each other, to maintain the social distance due to CORONA virus pandemic. Let three students sit at points A, Band C whose coordinates are (4, -3), (7,3) and (8, 5) respectively.

Based on the above information, answer the following questions.
(i) The distance between A and C is 

(ii) If an invigilator at the point I, lying on the straight line joining Band C such that it divides the distance between them in the ratio of 1 : 2. Then coordinates of I are

(iii) The mid-point of the line segment joining A and C is

(iv) The ratio in which B divides the line segment joining A and C is

(v) The points A, Band C lie on