Embibe Experts Solutions for Chapter: Coordinate Geometry, Exercise 1: meghalaya board-2020

If the point $P(x,y)$ is equidistant from the points $A(5,1)$ and $B(1,5)$, then prove that $x=y$.

Find the value of  $\text{'}p\text{'}$ for which the given points $(-3,9), (2,p)$ and $(4,-5)$ are collinear.

The line segment joining $A(-2, 9)$ and $B(6, 3)$ is a diameter of a circle with center $C$. Find the coordinates of $C$.

Two vertices of a triangle are $\left(3, -5\right)$ and $\left(-7, 4\right).$ If its centroid is $\left(2, -1\right)$, then find the third vertex.

Find the ratio in which the point $P\left(-6, a\right)$ divides the join of $A\left(-3, 1\right)$ and $B\left(-8, 9\right)$. Also, find the value of $a$.

If the area of a triangle is _____ square units, then its vertices are collinear.

Find the distance between the points $\left(5,8\right)$ and $\left(-3,2\right)$.

Find the coordinates of the centroid of the triangle whose vertices are $\left(-3,0\right), \left(5,-2\right), \left(-8,5\right)$.