Students of a school are standing in rows and columns In their playground for drill practice. $\mathrm{A}, \mathrm{B}, \mathrm{C}$and $\mathrm{D}$ are the position of the four students as shown in the figure below.

Mohit wants to stand in such a way that he is equidistance from each of the four students $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$. What should be the coordinate of his position?

A ball was thrown horizontally from the top of a building with a speed of $20 \mathrm{m}/\mathrm{s}$ . Its real time coordinates is $\left(ut, \frac{1}{2}g{t}^2\right)$ with respect to the person, $B$ who threw the ball from the top of building. $u$ is the velocity with which the ball was thrown and $g$ is the acceleration due to gravity.  The building is $60 \mathrm{m}$ tall. Consider $g=10 \mathrm{m}/{\mathrm{s}}^2$

If the distance of the ball from an observer standing at point $A$ (at the bottom of the building) at the end of $2$ seconds since the ball was thrown is $a\sqrt{2},$ Then find $a.$

The coordinates of Bengaluru and New Delhi are $(12.97° \mathrm{N}, 77.59° \mathrm{E})$ and $(28.61° \mathrm{N}, 77.21° \mathrm{E})$ respectively. The distance between $1°$ latitude is $109.20 \mathrm{km}$ and the distance between $1°$ longitude is $86.46 \mathrm{km}$.

Estimate the straight line distance between Bengaluru and New Delhi.

The coordinates of three towns, Kannur, Madikeri and Hassan are given below. Show that these towns lie on a straight line. 

Kannur:$11.8745° \mathrm{N}, 75.3704° \mathrm{E}$
Madikeri:$12.4244° \mathrm{N}, 75.7382° \mathrm{E}$
Hasan: $13.0033° \mathrm{N}, 76.1004° \mathrm{E}$

The distance between $1°$ latitude is $109.2 \mathrm{km}$ and that of $1°$ longitude is $86.46 \mathrm{km}$

The cities, Indore, Hyderabad and Chennai lie along a straight line. 

The coordinates of Indore, Hyderabad and Chennai are $(22.7196° \mathrm{N}, 75.8577° \mathrm{E}), (17.3850° \mathrm{N}, 78.4867° \mathrm{E})$ and$(13.0827° \mathrm{N}, 80.2707° \mathrm{E})$ respectively.  

Find the ratio of distances of Indore - Hyderabad to that of Hyderabad - Chennai.

$1°$ latitude $=109.2 \mathrm{km}$ and $1°$ longitude $=86.46 \mathrm{km}$

A student made a cutout of a triangle from a poster card and pasted it on graph sheet. The vertices of triangle are $\left(3,7\right), \left(14,15\right),$ and $\left(15,1\right)$. 

Find the area of the cardboard cutout, if the units used in the graph sheet is in centimetres.

The figure below shows a playground and a circular running track in the middle. Two diametrically opposite locations on the circular track is marked in the figure. The distance to these locations from bottom-left corner is also given.  

Find the length of the circular track.

Below is the sketch of land in the shape of quadrilateral. The horizontal and vertical distance relative to bottom-left corner of the land is shown in the sketch.

Find the area of the land.