COORDINATE GEOMETRY

The mid-point of the line segment joining the points \(P(-4,5)\) and \(Q(4,6)\) lies on:

The coordinates of the end points of a diameter of a circle are \((2,4)\) and \((-3,-1)\). The length of its radius is:

The coordinates of the end points of a diameter of a circle are \((5,-2)\) and \((5,2)\). The length of the radius of the circle is:

The points \((-5,0)\), \((5,0)\) and \((0,4)\) are the vertices of a triangle which is a/an:

The perimeter of the triangle formed by the vertices \((0,0)\), \((2,0)\) and \((0,2)\) is:

The line represented by \(\frac{x}{4}+\frac{y}{6}=1\), intersects x-axis and y-axis respectively at \(P\) and \(Q\). The coordinates of the mid-point of line segment \(PQ\) are:

Two of the vertices of \(\triangle PQR\) are \(P(-1,5)\) and \(Q(5,2)\). The coordinates of a point which divides \(PQ\) in the ratio \(2:1\) are:

\(AOBC\) is a rectangle whose three vertices are \(A(0,2)\), \(O(0,0)\) and \(B(4,0)\). The square of the length of its diagonal is equal to:

If the mid-point of the line segment joining the points \((a,4)\) and \((2,2b)\) is \((2,6)\), then the value of \((a+b)\) is:

The distance of the point \((4,0)\) from x-axis is:

The distance of which of the following points from origin is less than 5 units?

In the figure given below, points \(P,Q,R\) divide the line segment \(AB\) in four equal parts. The point \(Q\) divides \(PB\) in the ratio:

The point \(P\) divides the line segment \(AB\) in the ratio \(3:1\) as shown below \([A-P-B]\). The value of \(\frac{AB}{PB}\) is:

The distance of the point \(A(-3,-4)\) from x-axis is:

The distance of point \((a,-b)\) from x-axis is:

Find the length of the median through the vertex \(B\) of \(\triangle ABC\) with vertices \(A(9,-2)\), \(B(-3,7)\) and \(C(-1,10)\).

The coordinates of the end points of the line segment \(AB\) are \(A(-2,-2)\) and \(B(2,-4)\). \(P\) is the point on \(AB\) such that \(BP=\frac47AB\). Find the coordinates of point \(P\).

Find the coordinates of a point \(P\) which is equidistant from points with coordinates \(A(7,1)\) and \(B(3,5)\), such that its abscissa is 2 more than its ordinate.

Find the ratio in which the y-axis divides the line segment joining the points \((5,-6)\) and \((-1,-4)\). Also find the point of intersection.

If the mid-point of the line segment joining the points \(A(3,4)\) and \(B(k,6)\) is \(P(x,y)\) and \(x+y-10=0\), then find the value of \(k\).

If \((a,b)\) is the mid-point of the line segment joining the points \(A(10,-6)\) and \(B(k,4)\) and \(a-2b=18\), then find the value of \(k\).

Find the coordinates of the points which divide the line segment joining \(A(-2,2)\) and \(B(2,8)\) into four equal parts.

Find a relation between \(x\) and \(y\) such that \(P(x,y)\) is equidistant from the points \(A(3,5)\) and \(B(7,1)\). Hence, write the coordinates of the points on x-axis and y-axis which are equidistant from points \(A\) and \(B\).