Find the area of the triangle formed by the points (1, –1), (–4, 6) and (–3, –5)

Determine whether the sets of points are collinear? \((-\frac12 ,3)\), (- 5, 6) and (-8, 8)

Vertices of given triangles are taken in order and their areas are provided aside. In each case, find the value of ‘p’?

S.No	Vertices	Area (sq.units)
(i)	(0, 0), (p, 8), (6, 2)	20
(ii)	(p, p), (5, 6), (5, -2)	32

The line r passes through the points (–2, 2) and (5, 8) and the line s passes through the points (–8, 7) and (–2, 0). Is the line r perpendicular to s ?

The line p passes through the points (3, - 2), (12, 4) and the line q passes through the points (6, -2) and (12, 2). Is parallel to q ?

Show that the points (-2, 5), (6, -1) and (2, 2) are collinear

What is the slope of a line whose inclination with positive direction of x - axis is 90⁰

What is the inclination of a line whose slope is 0

Find the slope of a line joining the points \(\left( 5,\sqrt { 5 } \right) \) with the origin

What is the slope of a line perpendicular to the line joining A(5, 1) and P where P is the mid-point of the segment joining (4, 2) and (-6, 4).

Show that the given points are collinear: (-3, -4) , (7, 2) and (12, 5)

If the three points (3, - 1) , (a, 3) and (1, - 3) are collinear, find the value of a.

The line through the points (-2, a) and (9, 3) has slope - \(\frac { 1 }{ 2 } \). Find the value of a.

The line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24) . Find the value of x.

Show that the given vertices form a right angled triangle and check whether its satisfies Pythagoras theorem A(1, - 4) , B(2, - 3) and C(4, - 7)