Question

If M is any point exactly in between Noida and Delhi,  then coordinates of M are (1 Point) (6.5, 9) (5, 5) (6,6) (3, 3)​

Answer 1

Answer:

(i) (i) (0,7,−10),(1,6,−6) and (4,9,−6) are the vertices of an isosceles triangle

(ii) (0,7,10),(−1,6,6) and (−4,9,6) are the vertices of a right angled triangle

(iii) (−1,2,1),(1,−2,5),(4,−7,8) and (2,−3,4) are the vertices of a parallelogram and (4,9,−6) are the vertices of an isosceles triangle.

Answer 2

Explanation 1:

From the diagram, we can clearly see that Anmol starts his journey from 0 $(0,0)$ towards City A $(2,y)$. The distance between point O to A is also given, which is $2\sqrt{2}km$.

Applying distance formula between O and A, we get

$D=\sqrt{(x_{2}- x_{1} )^{2}+ (y_{2}- y_{1} )^{2} }$

We have, $D=2\sqrt{2}$   $;$  $(x_{1}, y_{1} )=(0,0)$   $;$   $(x_{2}, y_{2} )=(2,y)$

$2\sqrt{2}=\sqrt{(2-0)^{2}+ (y-0)^{2} }$

$4+y^{2}=8$

$y^{2}=4$

$y=2$

Hence, the value of y is (a) 2.

Explanation 2

We have, the coordinates of point A as $(2,2)$ and point B as $(x,8)$. We also have the distance between point A and B as $6\sqrt{2}km$.

Applying distance formula,

$D=\sqrt{(x_{2}- x_{1} )^{2}+ (y_{2}- y_{1} )^{2} }$

Here, $D=6\sqrt{2}km$    $;$  $(x_{1}, y_{1} )=(2,2)$    $;$  $(x_{2}, y_{2} )=(x,8)$

$6\sqrt{2}=\sqrt{(x-2)^{2} +(8-2)^{2} }$

$x^{2} -4x+4+36=72$

$x^{2} -4x-32=0$

$x^{2} -8x+4x-32=0$

$(x+4)(x-8)=0$

$x=8$

Hence, the value of x is (c) 8.

Explanation 3

We know, the coordinates of Noida are given as $(2,2)$ and of Delhi are $(8,8)$

Given, M is any point in between Noida and Delhi. Hence, applying

Mid-Point Formula, we get

$(x,y)=\frac{x_{1}+ x_{2} }{2}, \frac{y_{1}+ y_{2} }{2}$

We have, $(x_{1}, y_{1} )=(2,2)$  and $(x_{2}, y_{2} )=(8,8)$

$(x,y)=\frac{2+8}{2},\frac{2+8}{2}$

$(x,y)=(5,5)$

Hence, the coordinates of point M are $(5,5)$

Explanation 4

We know, coordinates of office are $(x_{1}, y_{1} )=(0,0)$ , coordinates of point M are$(x_{2}, y_{2} )=(5,5)$ and that of Noida are $(x_{3} ,y_{3} )=(2,2)$.

Lets assume, Noida divides the line joining between office and point M in the ratio  $m_{1}: m_{2}= k:1$.

Then, according to section formula, the coordinates of Noida are given by

$(x_{3} ,y_{3} )=\frac{m_{1} x_{2}+m_{2} x_{1} }{m_{1}+ m_{2} } ,\frac{m_{1} y_{2}+m_{2} y_{1} }{m_{1}+ m_{2} }$

Therefore,

$(2,2)=\frac{k(5)+1(0)}{k+1},\frac{k(5)+1(0)}{k+1}$

We get

$\frac{5k}{k+1}=2$

$5k=2k+2$

$3k=2$

$k=\frac{2}{3}$

Hence, Noida divides the line joining office and Delhi in the ratio (d) 2 : 3.

Explanation 5

M is a point very far away from his college as compared to his distance from Delhi so trying to go in the forward direction towards Delhi will be a good decision. (b)

Although your question is incomplete, you might be referring to the question below.

Anmol is driving his car on a straight road towards East from his office to Noida and then to Delhi, at some point, in between Noida and Delhi, he suddenly realizes that there is not enough petrol for the journey. Also, there is no petrol pump between these two cities. Based on the above information answer the following.

• The value of y is equal to

         a) 2   b) 3   c) 4   d) 5

• The value of x is equal to

         a) 4   b) 5   c) 8   d) 9

• If M is any point exactly in between Noida and Delhi, the the coordinates of M are

         a) (3 ,3)   b) (6.5 ,9)   c) (5 ,5)   d) (6 ,6)

• The ratio in which Noida divides the line joining the office and point M is

         a) 1:4   b) 2:1   c) 3:2   d) 2:3

• If Anmol analyses the CNG at the point M (the mid point of Noida-Delhi ) then what should be his decision.

          a) should travel back to office  

          b) should try his luck to move towards Delhi

          c) Should travel back to Noida

          d) None of the above.