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

Find the point on the$y-$axis which is equidistant from the point $\left(6,5\right)$ and $\left(-4,3\right)$.

Find the co-ordinate of mid point of the line joining points $\left(4,-1\right)$ and $\left(-2,-3\right)$.

Find the coordinates of the point which divides internally the line joining the points $\left(6,-9\right)$ and $\left(4,6\right)$ in the ratio $3:4$.

If $\left(1,1\right). \left(7,-3\right), \left(12,2\right) \text{and} \left(7,21\right)$ are the coordinates of the vertices of the quadrilateral, prove that the area of quadrilateral is $138$ square unit.

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

Find the values of $\mathrm{Y}$ for which the distance between the points $P(-2,3)$ and $Q(10,\mathrm{Y})$ is $10$ units.

Find the values of $k$ if the points $A(2,3), B\left(4,k\right)$ and $C(6,-3)$ are Collinear.

Check whether $\left(5, -2\right), \left(6, 4\right) \& \left(7, -2\right)$ are the vertices of an isosceles triangle.