Home
Class 11
MATHS
There are m points on the line AB and n ...

There are m points on the line AB and n points on the line AC, excluding the point A. Triangles are formed joining these points

A

`(mn)/(2)(m+n-2)`

B

`(mn)/(2)(m+n-1)`

C

`(mn)/(2)(m+n)`

D

`(mn)/(2)(m+n+1)`

Text Solution

Verified by Experts

A triangle can be constructed in the following ways:
(i) By taking tow points on AB and one point on AC,

(ii) By taking two points on AC and one point on AB. If point A is included, then total number of triangles
`=""^(m+1)C_(2)xx""^(n)C_(1)+""^(m)C_(1)xx""^(n)C_(2)`
`=((m+1)mn)/(2)+(mn(n-1))/(2)=(mn)/(2)=(m+n)`
Promotional Banner

Similar Questions

Explore conceptually related problems

There are m points on a straight line AB & n points on the line AC none of them being the point A. Tri- angles are formed with these points as vertices, when A is excluded (ii) A is included. The ratio of number of triangles in the two cases is

Straight lines are drawn by joining m points on a straight line of n points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no tow lines drawn are parallel and no these lines are concurrent). a. 4m n(m-1)(n-1) b. 1/2m n(m-1)(n-1) c. 1/2m^2n^2 d. 1/4m^2n^2

There are 10 points in a plane, out of which 6 are collinear. If N is the number of triangles formed by joining these points, then :