Basics of 2D Coordinate Geometry

If coordinates of A and B are $\left(5, 6\right)$ and $\left(9, 10\right)$ respectively then the length of line segment AB is:

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

The distance between points $(2, 5)$and $(7, -3)$ is

Locus of the centre of rolling circle in a plane will be

What is the distance of point $\left(5, 12\right)$ from the origin?

If the distance between two points $A\left(x, 10\right)$ and $B\left(7, 18\right)$ is $10 \mathrm{units}$, then find the distance between the point $C\left(2x, 10\right)$ and $D\left(8, 18\right)$. (Take $x>0$)

Line PQ is given as $(y+2)=3(x-1)$ Another line AB passes through a point $\left(-5,-6\right)$ and is parallel to PQ. Find the equation of line AB.

If a line has the equation $\left(y+4\right)=m\left(x-7\right)$ and it passes through the point $\left(-5,6\right).$ Then find the slope of this line

The point $(x,2)$ is at a distance of $8$ units from the line $9x+12y+15=0,$What is the value of $x$?

The three vertices $A,B,C$ of a parallelogram $ABCD$ are $(–2,–1),(3,0),(1,–2)$ respectively, find the co-ordinates of vertex $D$.

Find the ratio in which the segment joining$(-1,-12)$ and $(3,4)$ divided by the $x -$ axis ?

A line cuts the $x -$ axis at the point$(-3,0)$ and the  - axis at the point (0,6) . What is the equation of the line?

What is the equation of line which joins the points $A(-1,3)$ and $B(4,-2)$?

Find the equation of perpendicular bisector of the line joining $(5,6)$ and $(2,-2)$.

What is the equation of the perpendicular line to segment joining the points $A(0,4)$ and $B(-5,9)$ and passing through the point $P$. Point $P$ divides line segment $AB$ in the ratio $2:3$.  

A point $P(x+y,5)$ is equidistance from points $A(x,2)$ and $B(y,4)$ and distance of line $AB$ is $2\sqrt{5}$ units, then what is the length of line $AP$? 

A point$P(x, y)$ internally divides line segment $AB$ $5:2$ in the ratio and co-ordinates of points $A$ and $B$ is $\left(5,9\right)$ $\left(5,-19\right)$ and then which of the following equation of line will pass through point $P$?

In what ratio does the point $(1, 6)$ divides the line segment joining points $(4, 5)$ and $(-8, 9)$.

Find the ratio in which the segment $(2, -4)$ and $(-1, 8)$ is divided by $x-$ axis.

If the point $P(-3, 2)$ divides the line segment forming $A(3, 6)$ and $B(a, b)$ in the ratio $3:4$. Then, find $B$ point.