Question

Centonion Public School Society, which has so many schools in different cities of India. One of the branch of Centonion Public School is in Meerut. In that School hundreds of students are in a classroom. Out of them one of the girl is standing in the ground having coordinates (3, 4) facing towards west. She moves 5 units in straight line then take right and moves 4 units and stop. Now, she is at her coaching centre. The representation of the above situation on the coordinate axes is shown below: Based on the above information give the answer of the following questions.

46. What is the shortest distance between her school and coaching centre? a) √41 units b) 3 units c) 6 units d) 7 units

47. Suppose point D(1, 4) divide the line segment AB in theratio k:1, then find the value of k a) 3 b) 3/2 c) 2 d) ½

48. If we draw perpendicular lines from points A and B to the x-axis, the region covered by these perpendicular lines is: a) 4 sq. units b) 5 sq. units c) 20 sq. units d) 10 sq. units

49. Find the area of triangle ABC a) 4 sq. units b) 5 sq. units c) 20 sq. units d) 10 sq. units

50. Find the image of the midpoint of AB with respect to x-axis a) ( 1 2 , −4) c) (− 1 2 , 4) b) ( 1 2 , 4) d) (− 1 2 , −4)​

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

Given:

Centonion Public School Society, which has so many schools in different cities of India. One of the branches of Centonion Public School is in Meerut. In that School, hundreds of students are in a classroom. Out of them one of the girls is standing in the ground having coordinates (3, 4) facing towards the west. She moves 5 units in a straight line then take right and moves 4 units and stop. Now, she is at her coaching centre. The representation of the above situation on the coordinate axes is shown below

To Find:

46. What is the shortest distance between her school and the coaching centre?

a) √41 units

b) 3 units

c) 6 units

d) 7 units

47. Suppose point D(1, 4) divide the line segment AB in the ratio k:1, then find the value of k

a) 3

b) 3/2

c) 2

d) ½

48. If we draw perpendicular lines from points A and B to the x-axis, the region covered by these perpendicular lines is:

a) 4 sq. units

b) 5 sq. units

c) 20 sq. units

d) 10 sq. units

49. Find the area of triangle ABC

a) 4 sq. units

b) 5 sq. units

c) 20 sq. units

d) 10 sq. units

50. Find the image of the midpoint of AB with respect to the x-axis

a) ( 1/2 , −4)

c) (− 1/2 , 4)

b) ( 1/2 , 4)

d) (− 1/2 , −4)​

Solution:

first, we will locate the point of her coaching centre which will be (-2,8)

(46) The shortest distance between her school and coaching centre is the distance between (-2,8) and(3,4)

Using the distance formula distance d can be calculated as

$d=\sqrt{(-2-3)^2+(8-4)^2}\\=\sqrt{25+16} \\=\sqrt{41}$

Hence, the correct option will be (a).

(47) If the point (1,4) divides the line AB into k:1 ratio then

$ratio=\frac{1-(-2)}{3-1}\\=\frac{3}{2}\\=3:2\\=\frac{3}{2}:1$

Hence, the correct option is (b).

(48) The region will form a rectangle with width as 4 units and length as 5 units so,

$A=4*5\\=20unit^2$

Hence, the correct option will be (c).

(49) The area of a triangle which is a right-angled triangle will be

$A=\frac{1}{2} *5*4\\=10unit^2$

Hence, the correct option is (d).

(50) The midpoint of A and B will be [(3-2)/2,(4+4)/2]=(1/2,4)

whose image on the x-axis will be (-1/2,-4).

Hence, the correct option will be (d).