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

 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 $B$.

Show that the triangle whose vertices are $A(8,-4), B(9, 5) \mathrm{and} \mathrm{C}(0, 4)$ is an isosceles triangle.

Find the co-ordinates of the mid-point of the line segment joining the points $\left(2, 3\right)$ and $\left(4, 7\right)$.

Find the coordinates of the point which divides the line segment joining the point $A\left(4, -3\right) \& B\left(8, 5\right)$ in ratio $3:1$ internally.

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

In what ratio does the point $\left(-4,6\right)$ divide the line segment joining the points $A\left(-6,10\right)$ and $B\left(3, -8\right)$ internally?

Find the point on the $x-axis$which is equidistant from $(2,-5)$ and $(-2, 9).$

The point $\left(x,y\right)$ is equidistant from the points $\left(7,1\right)$ and $\left(3,5\right)$, Then