we know that intercept form of line is
we know that
In this problem
On squaring both the sides
we will get
Hence proved

Let suppose foot of perpendicular is
We can say that line passing through point is perpendicular to line passing through point
Now,
Slope of line passing through point is ,
And
Slope of line passing through point is ,
lines are perpendicular
Therefore,
Now, equation of line passing through point (2 ,3) and slope with 1
-(i)
Now,...

Given equations of lines are and
We can rewrite the equation as
Now, we know that
In equation
Similarly,
in the equation
Now,
Hence proved

We can say that line passing through point is perpendicular to line
Now,
The slope of the line passing through the point is ,
lines are perpendicular
Therefore,
- (i)
Now, the point also lies on the line
Therefore,
Therefore, the value of m and C is respectively

Let suppose the foot of perpendicular is
We can say that line passing through the point is perpendicular to the line
Now,
The slope of the line is ,
And
The slope of the line passing through the point is,
lines are perpendicular
Therefore,
Now, the point also lies on the line
Therefore,
On solving equation (i) and (ii)
we will get
Therefore,

Right bisector means perpendicular line which divides the line segment into two equal parts
Now, lines are perpendicular which means their slopes are negative times inverse of each other
Slope of line passing through points and is
Therefore, Slope of bisector line is
Now, let (h , k) be the point of intersection of two lines
It is given that point (h,k) divides the line segment...

Let the slope of two lines are respectively
It is given the lines intersects each other at an angle of and slope of the line is 2
Now,
Now, the equation of line passing through point (2 ,3) and with slope is
-(i)
Similarly,
Now , equation of line passing through point (2 ,3) and with slope is
-(ii)
Therefore,...

It is given that line is parallel to the line
Therefore, their slopes are equal
The slope of line ,
Let the slope of other line be m
Then,
Now, the equation of the line passing through the point and with slope is
Hence proved

Line passing through points ( h ,3) and (4 ,1)
Therefore,Slope of the line is
This line intersects the line at right angle
Therefore, the Slope of both the lines are negative times inverse of each other
Slope of line ,
Now,
Therefore, the value of h is

Given equation of lines are
and
Slope of line is,
And
Slope of line is ,
Now, if is the angle between the lines
Then,
Therefore, the angle between the lines is

It is given that line is perpendicular to the line
we can rewrite it as
Slope of line ( m' ) =
Now,
The slope of the line is
Now, the equation of the line with intercept i.e. (3, 0) and with slope -7 is

It is given that line is parallel to line which implies that the slopes of both the lines are equal
we can rewrite it as
The slope of line =
Now, the equation of the line passing through the point and with slope is
Therefore, the equation of the line is

Given equations of lines are
and
it is given that these lines are parallel
Therefore,
Now,
Therefore, the distance between two lines is

Given equation of line is
we can rewrite it as
Now, we know that
In this problem A = 4 , B = 3 C = -12 and d = 4
point is on x-axis therefore = (x ,0)
Now,
Now if x > 3
Then,
Therefore, point is (8,0)
and if x < 3
Then,
Therefore, point is (-2,0)
Therefore, the points on the x-axis, whose distances from the line are units are (8 , 0) and (-2 , 0)

Given the equation of the line is
we can rewrite it as
Now, we know that
where A and B are the coefficients of x and y and C is some constant and is point from which we need to find the distance
In this problem A = 12 , B = -5 , c = 82 and = (-1 , 1)
Therefore,
Therefore, the distance of the point from the line is 5 units

Given equation is
Coefficient of x is 1 and y is -1
Therefore,
Now, Divide both the sides by
we wiil get
we can rewrite it as
Now, we know that normal form of line is
Where is the angle between perpendicular and the positive x-axis and p is the perpendicular distance from the origin
On compairing equation (i) and (ii)
we wiil get
Therefore, the angle between perpendicular...

Given equation is
we can rewrite it as
Coefficient of x is 0 and y is 1
Therefore,
Now, Divide both the sides by 1
we will get
we can rewrite it as
Now, we know that normal form of line is
Where is the angle between perpendicular and the positive x-axis and p is the perpendicular distance from the origin
On comparing equation (i) and (ii)
we wiil get
Therefore, the...

Given equation is
we can rewrite it as
Coefficient of x is -1 and y is
Therefore,
Now, Divide both the sides by 2
we will get
we can rewrite it as
Now, we know that the normal form of the line is
Where is the angle between perpendicular and the positive x-axis and p is the perpendicular distance from the origin
On comparing equation (i) and (ii)
we wiil get
Therefore, the...

**Q: 2 ** Reduce the following equations into intercept form and find their intercepts on the axes.

(iii)

Given equation is
we can rewrite it as
Therefore, intercepts on y-axis are
and there is no intercept on x-axis

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