Find the distance between the points (–4, 3), (2, –3).

Show that the points A(–4, –3), B(3, 1), C(3, 6), D(–4, 2) taken in that order form the vertices of a parallelogram.

Calculate the distance between the points A (7, 3) and B which lies on the x-axis whose abscissa is 11.

The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, What are the coordinates of A?

The point (x, y) is equidistant from the points (3, 4) and (–5, 6). Find a relation between x and y.

Let A(2, 3) and B(2, –4) be two points. If P lies on the x-axis, such that AP = \(\frac{3}{7}\) AB, find the coordinates of P.

Find the perimeter of the triangle whose vertices are(3, 2), (7, 2) and (7, 5).

Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, –4) and (5, -6)

The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.

Show that the following points taken in order form an equilateral triangle in each case
\(A\left( \sqrt { 3 } ,2 \right) ,B\left( 0,1 \right) ,C\left( 0,3 \right) \)