In what ratio is the line joining (1,2) (4,3) divided by the line joining (2,3) (4,1)??
Here lines AB and CD intersect each other at point O as shown below:
Slope of the line AB =
Equation of line AB passing through the points A(2, 3) having the slope -1 is;
......(i)
Also slope of the line CD =
Equation of line CD passing through the points C(1, 2) having the slope is;
....(ii)
Now solving equation (i) and (ii) we have;
then,
Therefore both lines intersect at point .
Now the distance between the point and = CO =
Also the distance between the point and = DO =
So required ratio =
Hence O is the mid point of CD.
Slope of the line AB =
Equation of line AB passing through the points A(2, 3) having the slope -1 is;
......(i)
Also slope of the line CD =
Equation of line CD passing through the points C(1, 2) having the slope is;
....(ii)
Now solving equation (i) and (ii) we have;
then,
Therefore both lines intersect at point .
Now the distance between the point and = CO =
Also the distance between the point and = DO =
So required ratio =
Hence O is the mid point of CD.