Question

Barun lives in Jaipur in Vaishali. Satellite image of his colony is shown in given figure. In this view, his house is pointed out by a flag, which is situated at the point of intersection of x and y - axes. If he goes 2 cm east and 3 cm north from the house, then he reaches to a grocery store, If he goes 4 cm west and 6 cm south from the house, then he reaches to his office. If he goes 6 cm east and 8 cm south from the house, then he reaches to a food court. If he goes 6 cm west and 8 cm north from the house, he reaches to a his kid’s school. Based on the above information, answer the following questions.

46. What is the distance between grocery store and food court? (a) 137 cm (b) 129 cm (c) 8 15 cm (d) 16 3 cm

47. What is the distance of the school from the house? (a) 10 cm (b) 15 cm (c) 20 cm (d) 25 cm

48. If the grocery store and office lie on a line, what is the ratio of distance of house from grocery store to that from office ? (a) 2 :1 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1

49. What is the ratio of distances of house from school to food court. (a) 1 :1 (b) 2 : 1 (c) 3 : 1 (d) 4 : 1

50. What shape is formed by the coordinates of positions of school, grocery store, food court and office? (a) square (b) rectangle (c) rhombus (d) quadrilatera​

Answer 1

Given:

Barun lives in Jaipur in Vaishali. A satellite image of his colony is shown in the given figure. In this view, his house is pointed out by a flag, which is situated at the point of intersection of x and y - axes. If he goes 2 cm east and 3 cm north from the house, then he reaches a grocery store, If he goes 4 cm west and 6 cm south from the house, then he reaches his office. If he goes 6 cm east and 8 cm south from the house, then he reaches a food court. If he goes 6 cm west and 8 cm north from the house, he reaches his kid’s school.

To Find:

46. What is the distance between the grocery store and the food court? (a) 11.7 cm (b) 12.9 cm (c) 8.15 cm (d) 16.3 cm

47. What is the distance of the school from the house? (a) 10 cm (b) 15 cm (c) 20 cm (d) 25 cm

48. If the grocery store and office lie on a line, what is the ratio of the distance of the house from the grocery store to that from the office? (a) 2 :1 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1

49. What is the ratio of distances of the house from school to the food court. (a) 1 :1 (b) 2 : 1 (c) 3 : 1 (d) 4 : 1

50. What shape is formed by the coordinates of positions of school, grocery store, food court and office? (a) square (b) rectangle (c) rhombus (d) quadrilateral​

Solution:

Before doing the calculation it would be easy for us to first draw a rough graph of all the places that Barun goes and name the coordinates with the first letter of the place

(46) Now the distance between the grocery store(GS) and food court(FC) will be

$D=\sqrt{(8+3)^2+4^2}\\=\sqrt{121+16} \\=\sqrt{137}\\=11.7 cm$

Hence, option(a) is the correct answer.

(47) Now the distance between the school(S) and the House(H) will be$D=\sqrt{8^2+6^2}\\=\sqrt{64+36}\\=\sqrt{100} \\=10cm$

Hence, option(a) is the correct answer.

(48) The ratio will be

$D_{1}=\sqrt{3^2+2^2}\\=\sqrt{13}cm\\D_{2}=\sqrt{4^2+6^2}\\=2\sqrt{13} cm$

Hence, the ratio will be 2:1 so the correct option will be (a).

(49) As we can see that to go to school or food court we need to walk 5 and then turn and walk 8 in both cases so it will be a 1:1 ratio.

Hence, the correct option is (a).

(50) By observing the drawn diagram it can be observed that a quadrilateral shape is being formed.

Hence, the correct option is (d).

Answer 2

Answer:

(1) =(a)

(2) =(a)

(3) =(a)

(4) =(a)

(5) =(d)