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.

Below is the speed-time graph of a bus travelling from one location to another. The bus started from $A$ and stopped at $B$.

Find the distance travelled by the bus.

A cyclist started from home, and travelled $4 \mathrm{km}$ due North and then travelled due East for $3 \mathrm{km}$ . The cyclist then visited his friend, who is at$10 \mathrm{km}$ North, $11 \mathrm{km}$ East with respect to cyclist's home location.

If the whole journey took $1 \mathrm{hour}$ what is the cyclist's average speed in $\mathrm{km}/\mathrm{h}$?