Find the value of x for which the points (x, – 1), (2, 1) and (4, 5) are collinear.

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right-angled triangle.

Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram.

Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).