Show that (4, 3) is the centre of the circle passing through the points (9, 3), (7, –1), (–1, 3). Find the radius.

Verify that the following points taken in order form the vertices of a rhombus.
A(3, –2), B (7, 6),C (–1, 2) and D (–5, –6)

Verify that the following points taken in order form the vertices of a rhombus.
A (1, 1), B(2, 1),C (2, 2) and D(1, 2)

A(–1, 1), B(1, 3) and C(3, a) respectively and if AB = BC, then find ‘a’.

(i) Where do the following points lie?
P (0, -4), Q(0, -1), R(0, 3), S(0, 6).
(ii) Find the distance between the following points using coordinates given in question
(a) P and R
(b) Q and S
(iii) Draw the line diagram for the given above points.

Plot the points A( 1, 0), B ( -7, 2), C (-3, 7) on a graph sheet and join them to form a triangle.
Plot the point G ( -3, 3).
Join AG and extend it to intersect BC at D.
Join BG and extend it to intersect AC at E.
What do you infer when you measure the distance between BD and DC and the distance between CE and EA?
Using distance formula find the lengths of CG and GF, where F in on AB.
Write your inference about AG: GD, BG: GE and CG: GF.

The mid-points of the sides of a triangle are (5, 1), (3, −5) and (−5, −1). Find the coordinates of the vertices of the triangle.

Find the points of trisection of the line segment joining (−2, −1) and (4, 8)

In what ratio does the point P(–2, 4) divide the line segment joining the points A(–3, 6) and B(1, –2) internally?

What are the coordinates of B if point P(−2, 3) divides the line segment joining A(−3, 5) and B internally in the ratio 1 : 6?