EQUATION OF LINE WHICH IS PARALLEL AND PERPENDICULAR TO THE LINE

Equations of Line Which is Parallel and Perpendicular to the Line

Here we are going to see, how to find the equation of the line which is parallel and perpendicular to the line.

Equations of Line Which is Parallel and Perpendicular to the Line - Examples

If two lines are parallel,

m1  =  m2

If two lines are perpendicular,

m1 m=  -1

Question 1 :

Find the equation of the line in the xy-plane that contains the point (3, 2) and that is parallel to the line y = 4x − 1.

Solution :

Since the required line is parallel to the line y = 4x - 1

m = 4

(y - y1)  =  m(x - x1)

(y - 2)  =  4(x - 3)

y - 2  =  4x - 12

4x - y - 12 + 2  =  0

4x - y - 10  =  0

Question 2 :

Find the equation of the line that contains the point (2, 3) and that is parallel to the line containing the points (7, 1) and (5, 6).

Solution :

Slope of the line containing the points (7, 1) and )(5, 6)

m  =  (y2 - y1)/(x2 - x1)

m  =  (6 - 1)/(5 - 7)

m  =  4/(-2)

m  =  -2

Equation of the line :

(y - y1)  =  m(x - x1)

(y - 3)  =  -2(x - 2)

y - 3  =  -2x + 4

2x + y - 3 - 4  =  0

2x + y - 7  =  0

Question 3 :

Find the equation of the line in the xy-plane that contains the point (4, 1) and that is perpendicular to the line whose equation is y = 3x + 5.

Solution :

The required line is perpendicular to the line y = 3x + 5

Slope (m)  =  3

Slope of required line  =  -1/3

Equation of the line :

(y - y1)  =  m(x - x1

Point  => (4, 1) and slope m  =  -1/3

(y - 1)  =  (-1/3)(x - 4)

3(y - 1)  =  -1(x - 4)

3y - 3  =  -x + 4

x + 3y - 3 - 4  =  0

x + 3y - 7  =  0

Question 4 :

Find a number t such that the line in the xy plane containing the points (t, 4) and (2,−1) is perpendicular to the line y = 6x − 7.

Solution :

Slope of the line containing the points (t, 4) and (2, -1)

m  =  (y2 - y1)/(x2 - x1)

m  =  (-1 - 4) / (2 - t)

m  =  -5/(2 - t)

Slope of the given line :

y = 6x − 7

m  =  6

Slope of line perpendicular to the line y = 6x - 7 is -1/6

-1/6  =  -5/(2 - t)

-1(2 - t)  =  -5(6)

-2 + t  =  -30

t  =  -30 + 2

t  =  -30

After having gone through the stuff given above, we hope that the students would have understood "Equations of Line Which is Parallel and Perpendicular to the Line".

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