Embibe Experts Solutions for Chapter: Coordinate Geometry, Exercise 1: Exercise

Domlur and RajaRajeshwari Nagar  are two suburbs in Bengaluru. The GPS coordinates of Domlur is $\left(12.96°\mathrm{N},77.64°\mathrm{E}\right)$ and that of RjaRajeshwari Nagar is $\left(12.92°\mathrm{N}, 77.52°\mathrm{E}\right)$ The distance between $1°$ longitudes is $95 \mathrm{km}$ and the distance between by $1°$ latitude is $110 \mathrm{km}.$

What is the shortest distance between the two locations?

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 $a.$

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 $\mathrm{km}/\mathrm{h}$?