The Point and Straight line Concept with PYQ

There are 10 points in a plane out of these points no three are in the same straight line except 4 points which are collinear. How many (i) straight lines (ii) trian-gles (iii) quadrilateral, by joining them?

There are ten points in a plane. Of these ten points, four points are in a straight line and with the exceptionof these four points, on three points are in the same straight line. Find i. the number of triangles formed, ii the number of straight lines formed iii the number of quadrilaterals formed, by joining these ten points.

There are 15 points in a plane, no three of which are in a straight line except 4, all of which are in a straight line. The number of triangles that can be formed by using these 15 points is:

There are 10 points on a straight line AB and 8 on another straight line AC, none of them being A. How many triangles can be formed with these points as vertices?

The number of straight lines that can be formed by joining 20 points no three of which are in the same straight lines except 4 of them which are in the same line

There are 15 points in a plane, no three of which are in the same straight line with the exception of 6, which are all in the same straight line. Find the number of i. straight lines formed, ii. number of triangles formed by joining these points.

If three or more points does not lie on the same straight line the points are called -

A straight line is drawn from a fixed point O meeting a fixed straight line in P . A point Q is taken on the line OP such that OP.OQ is constant. Show that the locus of Q is a circle.