Plot the points T(4,-2) and V(-2,4) on a cartesian plane. Whether these two coordinates locate the same point?

The points (3, -2) (-2, 8) and (0, 4) are three points in a plane. Show that these points are collinear.

A point R with x-coordinate 4 lies on the line segment joining the points P(2, -3, 4) and Q(8, 0, 10). Find the coordinates of the point R.

The cartesian coordinates of the point Q in the figure is

Find the vector and cartesian equations of the planes : (a) that passes through the point (1, 0, -2) and the normal to the plane is hati+hatj-hatk . (b) that passes through the point (1,4, 6) and the normal vector to the plane is hati-2hatj+hatk .

Find the equation of the plane passing through the point (-1,2, 1) and perpendicular to the line joining the points (-3, 1, 2) and (2, 3, 4). Find also the perpendicular distance of the origin from this plane.

Find the cartesian coordinates of the points whose polar coordinates are (5 sqrt(2), (pi)/(4))

Consider the cartesian plane R^2 and let X denote the subset of points for which both coordinates are integers. A coin of diameter 1/2 is tossed randomly onto the plane. Find probability p that the coin covers a point of X.

Show that the points A (4, 2), B (7, 5) and C (9, 7) are three points lying on a same line.

Find the polar coordinates of the points whose cartesian coordinates are (-3, 4)