Question

draw a line segment of 10 cm on a paper and do the following 1. Make perpendicular line from a points on the given line. 2.Make a line intersecting the given line at a given point. 3.Make a line parallel to the given line​

Answer 1

Answer:

For intersection point we must have two straight lines, for which 2 points from each straight line must be selected. Now selection of these points can be done in

m

C

2

×

n

C

2

ways. Now as shown in diagram these four points can give two different sets of straight lines, which generate two distinct points of intersection.

Then total number of points of intersection is

m

C

2

×

n

C

2

×2.

m

C

2

×

n

C

2

×2.=

2!

m(m−1)

×

2!

n(n−1)

×2=

2

1

mn(m−1)(n−1)

solution