Straight Line | Part-3 |Ex-2A

In the previous article, we discussed 9 short ans type questions of Short Answer Type Questions of Straight Line Chapter of Chhaya Mathematics, Class 11. In this article, we have solved few more.

19.A ray of light start from , reflect on axis at and hence passing through find the co-ordinates of

Solution.

According to the problem, lies on axis. Let the co-ordinates of be

and

Hence,

20. Find the equation to the straight lines which are at a distance of unit from the origin and which pass through the point of intersection of the lines and

Solution.

We have the equations of straight lines and

Solving and we get,

Now, the straight lines passing through the point of intersection of the given lines must pass through the point

Any straight line through the point can be written as where is the slope of the straight line.

Equation can be written as

Perpendicular distance from origin to the straight line is

According to the problem,

For the equation of straight line

For the equation of straight line

21. Find the equation of the straight line through the point of intersection of the lines and and through the centroid of the triangle whose vertices are and

Solution.

The equation of the straight line through the point of intersection of the lines and is

Now, centroid of the triangle whose vertices are and is

Since the straight line passes through the point , so

So, putting the value of , we get the required equation of the straight line which is

22. Examine whether the straight lines and are concurrent or not.

Solution.

Solving we get, Putting these values of in the straight line we get,

So, does not satisfy the equation of the third straight line and hence we can conclude that the straight lines and are not concurrent.

23. For what value of the three straight lines and pass through the same point ?

Solution.

Solving we get,

Since the three straight lines pass through the same point, so
the third straight line passes through the point

24. If the straight lines and are concurrent, show that the points and are collinear.

Solution.

Since the straight lines and are concurrent, suppose that the common point is

From we can say that the general solution of is and

Again, represents a straight line on which the points lie.

Hence, the points and are collinear.

25. Show that the equation of the straight line through and through the point of intersection of the lines and is

Solution.

Equation of any straight line passing through the point of intersection of intersection of the lines and is

Now, if the straight line passes through the point then

Now, putting the value of in we get