**Q : 20 **By using the concept of equation of a line, prove that the three points and are collinear.

Points are collinear means they lies on same line
Now, given points are and
Equation of line passing through point A and B is
Therefore, the equation of line passing through A and B is
Now, Equation of line passing through point B and C is
Therefore, Equation of line passing through point B and C is
When can clearly see that Equation of line passing through point A nd B ...

Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.

**Q : 19**** ** Point divides a line segment between the axes in the ratio . Find equation of the line.

Let the coordinates of Point A is (x,0) and of point B is (0,y)
It is given that point R(h , k) divides the line segment between the axes in the ratio
Therefore,
R(h , k)
Therefore, coordinates of point A is and of point B is
Now, slope of line passing through points and is
Now, equation of line passing through point and with slope is
Therefore, the equation of line is

**Q: 18 ** is the mid-point of a line segment between axes. Show that equation

of the line is .

Now, let coordinates of point A is (0 , y) and of point B is (x , 0)
The,
Therefore, the coordinates of point A is (0 , 2b) and of point B is (2a , 0)
Now, slope of line passing through points (0,2b) and (2a,0) is
Now, equation of line passing through point (2a,0) and with slope is
Hence proved

**Q : 17**** ** The owner of a milk store finds that, he can sell 980 litres of milk each week at and litres of milk each week at . Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at ?

It is given that the owner of a milk store sell
980 litres milk each week at
and litres of milk each week at
Now, if we assume the rate of milk as x-axis and Litres of milk as y-axis
Then, we will get coordinates of two points i.e. (14, 980) and (16, 1220)
Now, the relation between litres of milk and Rs/litres is given by equation
Now, at he could sell
He could sell...

**Q : 16 ** The length (in centimetre) of a copper rod is a linear function of its Celsius temperature . In an experiment, if when and when , express in terms of .

It is given that
If then
and If then
Now, if assume C along x-axis and L along y-axis
Then, we will get coordinates of two points (20 , 124.942) and (110 , 125.134)
Now, the relation between C and L is given by equation
Which is the required relation

**Q: 15 ** The perpendicular from the origin to a line meets it at the point , find the equation of the line.

Let the slope of the line is m
and slope of a perpendicular line is which passes through the origin (0, 0) and (-2, 9) is
Now, the slope of the line is
Now, the equation of line passes through the point (-2, 9) and with slope is
Therefore, the equation of the line is

**Q : 14 **. Find equation of the line through the point making an angle with the positive -axis. Also, find the equation of line parallel to it and crossing the -axis at a distance of units below the origin.

We know that
Now, equation of line passing through point (0 , 2) and with slope is
Therefore, equation of line is -(i)
Now, It is given that line crossing the -axis at a distance of units below the origin which means coordinates are (0 ,-2)
This line is parallel to above line which means slope of both the lines are equal
Now, equation of line passing through point...

**Q : 13 ** Find equation of the line passing through the point and cutting off intercepts on the axes whose sum is .

Let (a, b) are the intercept on x and y axis respectively
Then, the equation of line is given by
It is given that
a + b = 9
b = 9 - a
Now,
It is given that line passes through point (2 ,2)
So,
case (i) a = 6 b = 3
case (ii) a = 3 , b = 6
Therefore, equation of line is 2x + y = 6 , x + 2y = 6

**Q: 12 ** Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point .

Let (a, b) are the intercept on x and y-axis respectively
Then, the equation of the line is given by
Intercepts are equal which means a = b
Now, it is given that line passes through the point (2,3)
Therefore,
therefore, equation of the line is

**Q : 11** A line perpendicular to the line segment joining the points and divides it in the ratio . Find the equation of the line.

Co-ordinates of point which divide line segment joining the points and in the ratio is
Let the slope of the perpendicular line is m
And Slope of line segment joining the points and is
Now, slope of perpendicular line is
Now, equation of line passing through point and with slope m is
equation of line passing through point and with slope is
Therefore, equation of line is

**Q : 10 ** Find the equation of the line passing through and perpendicular to the line through the points and .

It is given that the line passing through and perpendicular to the line through the points and
Let the slope of the line passing through the point (-3,5) is m and
Slope of line passing through points (2,5) and (-3,6)
Now this line is perpendicular to line passing through point (-3,5)
Therefore,
Now, equation of line passing through point and with slope m is
equation of line...

**Q : 9 ** The vertices of are and . Find equation of the median through the vertex .

The vertices of are and
Let m be RM b the median through vertex R
Coordinates of M (x, y ) =
Now, slope of line RM
Now, equation of line passing through point and with slope m is
equation of line passing through point (0 , 2) and with slope is
Therefore, equation of median is

Find the equation of the line which satisfy the given conditions:

**Q : 8 ** Perpendicular distance from the origin is units and the angle made by the perpendicular with the positive -axis is .

It is given that length of perpendicular is 5 units and angle made by the perpendicular with the positive -axis is
Therefore, equation of line is
In this case p = 5 and
Therefore, equation of the line is

Find the equation of the line which satisfy the given conditions:

**Q : 7 ** Passing through the points and .

We know that , equation of line passing through point and with slope m is given by
Now, it is given that line passes throught point (-1 ,1) and (2 , -4)
Now, equation of line passing through point (-1,1) and with slope is

Find the equation of the line which satisfy the given conditions:

**Q : 6 ** Intersecting the -axis at a distance of units above the origin and making an angle of with positive direction of the x-axis.

We know that , equation of line passing through point and with slope m is given by
Line Intersecting the y-axis at a distance of 2 units above the origin which means point is (0,2)
we know that
Now, the equation of the line passing through the point (0,2) and with slope is
Therefore, the equation of the line is

Find the equation of the line which satisfy the given conditions:

**Q : 5 ** Intersecting the -axis at a distance of units to the left of origin with slope .

We know that the equation of the line passing through the point and with slope m is given by
Line Intersecting the -axis at a distance of units to the left of origin which means the point is (-3,0)
Now, the equation of the line passing through the point (-3,0) and with slope -2 is
Therefore, the equation of the line is

Find the equation of the line which satisfy the given conditions:

**Q : 4 ** Passing through and inclined with the x-axis at an angle of .

We know that the equation of the line passing through the point and with slope m is given by
we know that
where is angle made by line with positive x-axis measure in the anti-clockwise direction
Now, the equation of the line passing through the point and with slope is
Therefore, the equation of the line is

Find the equation of the line which satisfy the given conditions:

**Q : 3**** **Passing through with slope .

We know that the equation of the line passing through the point and with slope m is given by
Now, the equation of the line passing through the point (0,0) and with slope m is
Therefore, the equation of the line is

Find the equation of the line which satisfy the given conditions:

**Q : 2** Passing through the point with slope .

We know that , equation of line passing through point and with slope m is given by
Now, equation of line passing through point (-4,3) and with slope is
Therefore, equation of the line is

Find the equation of the line which satisfy the given conditions:

**Q : 1 ** Write the equations for the -and -axes.

Equation of x-axis is y = 0
and
Equation of y-axis is x = 0

Exams

Articles

Questions