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

If $\mathrm{A}(\frac{m}{3}, 5)$ is the mid-point of the line segment joining the points $\mathrm{Q}(-6, 7)$ and $\mathrm{R}(-2, 3)$, then the value of $m$ is:

Triangle $ABC$ has vertices $A(3,-1), B(-3,-5)$ and $C(-1,5)$. Determine whether the triangle is a right triangle. Fully justify your answer.

Find the point on $y\text{-axis}$ which is equidistant from the points $\left(5,-2\right)$ and $\left(-3,2\right)$.

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.

 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 $B$.

$ABC$ is a triangle with vertices $A(1,0), B(5,9)\text{ and }C(9,0)$, Find the coordinates of the midpoints of the three sides of $ABC$.

Find the midpoint of pair of points: $\left(\frac{1}{4},\frac{1}{3}\right)\text{ and }\left(\frac{1}{3},\frac{1}{2}\right)$.