Introduction to parallel and perpendicular lines worksheet

Introduction to parallel and perpendicular lines worksheet
The equation of a straight line is an algebraic condition which is satisfied by every point on it.

The equation of a straight line is an algebraic condition which is satisfied by every point on it.

The various forms of straight lines

The equation of a straight line in various forms

Normal form of an equation is x cos a + y sin ß = p
Intercept form is x / a + y / b = 1
Symmetric form (x - x ) :cos ? = (y - y) :sin ?
General form of an equation ax + by +c = 0 (a2 + b2 ? 0 )
Parametic form x = x1 + r cos ? ; y= y1 + r sin ?

Parallel and Perpendicular Lines Worksheet : Slope

The slope of a straight line is represented in various forms from different forms of the equations

If the given vertices are (x1,y1) and (x2 ,y2 ) then the slope m is taken as y2 - y1 / x2 - x1

The slope of an equation can be represented as m = dy / dx where the derivatives are applied

If the line is in the form of a tanget equation y = mx +c then the slope will be equal to 'm'.

If the straight line makes an angle  theta with x axes then tan theta is called the slope.

If theta is acute, then tan theta is positive.

If theta is obtuse, then tan theta is negative.

If two lines are parallel, then they have same slope

If two lines are perpendicular, then m2 = -1/m1

where m2 is slope of second line

          m1 is slope of first line.

The slope concept for parallel and perpendicular lines are useful in  solving problems in worksheet.

Problems on Parallel and Perpendicular Lines Worksheet

Find the equation of line passing through ( 0,0) and parallel to   y = 3x + 2

Solution:  Given equation  is    y  = 3x +2

                slope of line  = m1  = 3

 As the lines where parallel  m1 = m2  = 3

Equation of line passing through (0,0)

is y = m2 x + c

As the line passes through origin , replace x and y values by 0,0 to find value of c

0 = 3(0) +c

c = 0

So equation of line parallel to y = 3x + 2 is   y = 3x

2) Find equation of line passing through (1,1) and perpendicular to y  = x + 3

Solution)  Given equation :  y = x + 3

           m1 =      Slope of line =  1

As lines where perpendicular , product of their slopes are equal to -1

                                               m1 *m2 = -1                   ( * represents multiplication symbol)

                                                   m2 = -1

Equation of line :   y  = m2 x + c

                           y = -x  +c

as the equation passes through (1,1) replace x and y by 1 , 1

                   1 = -1 + c

                     c = 2

Equation of required line is   y  = m2 x  + c

                                         y = -x + 2

Is this topic how to solve a math problem hard for you? Watch out for my coming posts.