Joins

if the straight line joining the points (3,4) and (2,-1) be parallel to the line joining the points (a,-2) and (4,-a), find the value of a.

The line joining the points (1,-5) and (4,-3) is parallel to the line joining the points .

Show that the line joining the points (4,-1) and (-3,3) is parallel to the line joining the points (8,0) and (1,4) .

Show that the line joining the points (4,-3) and (0,7) is perpendicular to the line joining the points (5,2) and (0,0) .

Show that the line joining the points (4,5) and (1,2) is parallel to the line joining the points (9,-2) and (12,1) .

Show that the line joining the points (2,-6) and (-4,-8) is perpendicular to the line joining the points (4,-2) and (6,-8) .

Line joining the points (3,-4) and (-2,6) is perpendicular to the line joining the points (-3,6) and (9,-18).

If four points be taken on a rectangular hyperbola such that the chord joining any two is perpendicular to the chord joining the other two, and if alpha,beta,gamma,delta be the inclinations to either asymptotes of the straight lines joining these points to the centre, then tanalphatanbetatangammatandelta is equal to

There are 10 points in a plane,no three of which are in the same straight line excepting 4 ,which ane collinear.Then,number of (A) straight lines formed by joining them is 40 (B) triangles formed by joining them is 116(C) straight lines formed by joining them is 45 (D) triangles formed by joining them is 120