Embibe Experts Solutions for Chapter: Coordinate Geometry, Exercise 1: CBSE-2018

Find the coordinates of a point $A$, where $AB$ is diameter of a circle whose centre is $\left(2,-3\right)$ and $B$ is the point $\left(1,4\right)$. 

Find the ratio in which the segment joining the point $\left(1,-3\right)$ and $\left(4,5\right)$ is divided by $x‐$axis? Also, find the coordinates of this point of the $x‐$axis.

The line segment joining the points $A(2,1)$ and $B(5,-8)$ is trisected at the points $P$ and $Q$ such that $P$ is nearer to $A$. If $P$ also
lies on the line given by $2x-y+k=0$, then find the value of $k$.

The distance between the points $\left(a\cos \theta +b\sin \theta , 0\right)$ and $\left(0, a\sin \theta -b\cos \theta \right)$, is 

If the point $P\left(k,0\right)$ divides the line segment joining the points $A\left(2,-2\right)$ and $B\left(-7,4\right)$ in the ratio $1:2$, then the value of $k$ is 

The value of $p$, for which the points $A\left(3,1\right)$, $B\left(5,p\right)$ and $C\left(7,-5\right)$ are collinear is

Find the area of triangle $\mathrm{PQR}$ formed by the points $\mathrm{P}\left(-5,7\right),\mathrm{Q}\left(-4,-5\right)$ and $\mathrm{R}\left(4,5\right)$.

 If the point $C\left(-1,2\right)$ divides internally the line segment joining $A\left(2,5\right)$ and $B\left(x,y\right)$ in the ratio $3:4$, find the coordinates of $B$.