In the previous article, we completed Circle Chapter of Chhaya Mathematics, Class 11. In this article, we have solved 9 short answer type questions of Straight Line Chapter.

1.Find the equation of the straight line passing through the points and and hence, show that the three points and are collinear.

Solution.

We know that the equation of the straight line in two-point form is where and are two given points on the line.

So, using we get the straight line passing through the points and which is

Hence , represents the equation of the straight line passing through the points and .

2nd Part :

Clearly, the points and lie on the straight line Now, we put in so that

and so the point lies on the straight line and so, we can conclude that the three points and are collinear.

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2. The vertices of a triangle are and Find the equation of the median through

Solution.

Let the triangle be denoted by where . So, the co-ordinates of the midpoint of the side are

Now, the median through must pass through the point and so, the equation of is

3. Find the equation of the straight line passing through the origin and dividing the segment of the straight line joining and internally in the ratio

Solution.

Suppose that the point divides the straight line joining and internally in the ratio

Now, the equation of the straight line passing through and is

Hence, the equation of the straight line passing through the origin and dividing the segment of the straight line joining and internally in the ratio is

4. A straight line passing through the point and is such that the portion of it intercepted between the axes is bisected at the point. Find the equation of the straight line and also its distance from the origin.

Solution.

Let the equation of straight line be

the straight line intersects at axis and axis at and respectively.

So, the midpoint of is

Now, according to the problem,

the equation of the straight line :

So, distance of the straight line from the origin is

5. A straight line passes through the point and is such that the portion of it intercepted between the axes is divided internally at the point in the ratio Find the equation of the line.

Solution.

Let the equation of straight line be

the straight line intersects at axis and axis at and respectively.

Suppose that the point divides the straight line joining and internally in the ratio

So, according to the problem,

the equation of the straight line

6. Find the locus of the middle point of the portion of the line-segment made by the straight line and the axes of co-ordinates.

Solution.

We have the given equation of straight line as follows :

the straight line intersects at axis and axis at and respectively.

Let be the co-ordinates of the midpoint

Hence, by we can conclude that the locus of the middle point of the portion of the line-segment made by the straight line is

7. A straight line moves in such a manner that the sum of the reciprocals of its intercepts upon the axes is always constant. Show that the line passes through a fixed a point.

Solution.

Suppose that the straight line cuts the axis and axis at and respectively.

So, the equation of the straight line is

According to the problem,

Now, comparing and we conclude that the straight line always passes through the point

8. The numerical value of the area of the triangle formed by a moving line on the co-ordinate axes is Find the locus of the middle point of the portion of the line intercepted between the axes.

Solution.

Suppose that the straight line cuts the axis and axis at and respectively.

So, the equation of the straight line is

If is the midpoint of , then

So, the area of

So, according to the problem,

Hence, the locus of is

9. The points and lie on the respective lines and find the equation of the straight line

Solution.

Since the points and lie on the respective lines and

From and we get

So, by we get,

Hence , the equation of the straight line is