11. For two lines, find Angle, intersection point and determine if parallel or perpendicular lines example ( Enter your problem )
  1. Find the acute angle between the lines x+3y+1=0 and 2x-y+4=0
  2. Find the point of intersection of the lines x+y=1 and x-y=1
  3. Determine if two lines are parallel 5x+2y-11=0 and 15x+6y-11=0
  4. Determine if two lines are perpendicular 5x+2y-11=0 and 2x-5y+11=0
Other related methods
  1. Distance, Slope of two points
  2. Points are Collinear or Triangle or Quadrilateral form
  3. Find Ratio of line joining AB and is divided by P
  4. Find Midpoint or Trisection points or equidistant points on X-Y axis
  5. Find Centroid, Circumcenter, Area of a triangle
  6. Find the equation of a line using slope, point, X-intercept, Y-intercept
  7. Find Slope, X-intercept, Y-intercept of a line
  8. Find the equation of a line passing through point of intersection of two lines and slope or a point
  9. Find the equation of a line passing through a point and parallel or perpendicular to Line-2 or point-2 and point-3
  10. Find the equation of a line passing through point of intersection of Line-1, Line-2 and parallel or perpendicular to Line-3
  11. For two lines, find Angle, intersection point and determine if parallel or perpendicular lines
  12. Reflection of points about x-axis, y-axis, origin

2. Find the point of intersection of the lines x+y=1 and x-y=1
(Previous example)
4. Determine if two lines are perpendicular 5x+2y-11=0 and 2x-5y+11=0
(Next example)

3. Determine if two lines are parallel 5x+2y-11=0 and 15x+6y-11=0





1. Determine if two lines are parallel 5x+2y-11=0 and 15x+6y-11=0

Solution:
When two lines are parallel, their slopes are equal.

1. Slope of line 5x+2y-11=0

5x+2y-11=0

:. 2y=-5x+11

:. y=-(5x)/(2)+11/2

:. Slope m_1=-5/2


2. Slope of line 15x+6y-11=0

15x+6y-11=0

:. 6y=-15x+11

:. y=-(5x)/(2)+11/6

:. Slope m_2=-5/2

Here m_1=m_2, so these two lines are parallel




2. Determine if two lines are parallel x-2y+15=0 and 2x-4y-4=0

Solution:
When two lines are parallel, their slopes are equal.

1. Slope of line x-2y+15=0

x-2y+15=0

:. 2y=x+15

:. y=(x)/(2)+15/2

:. Slope m_1=1/2


2. Slope of line 2x-4y-4=0

2x-4y-4=0

:. 4y=2x-4

:. y=(x)/(2)-1

:. Slope m_2=1/2

Here m_1=m_2, so these two lines are parallel




3. Determine if two lines are parallel x-y=1 and 2x-3y+1=0

Solution:
When two lines are parallel, their slopes are equal.

1. Slope of line x-y=1

x-y=1

:. y=x-1

:. Slope m_1=1


2. Slope of line 2x-3y+1=0

2x-3y+1=0

:. 3y=2x+1

:. y=(2x)/(3)+1/3

:. Slope m_2=2/3

Here m_1!=m_2, so these two lines are not parallel




4. Determine if two lines are parallel x-2y+15=0 and 3x+y-4=0

Solution:
When two lines are parallel, their slopes are equal.

1. Slope of line x-2y+15=0

x-2y+15=0

:. 2y=x+15

:. y=(x)/(2)+15/2

:. Slope m_1=1/2


2. Slope of line 3x+y-4=0

3x+y-4=0

:. y=-3x+4

:. Slope m_2=-3

Here m_1!=m_2, so these two lines are not parallel






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2. Find the point of intersection of the lines x+y=1 and x-y=1
(Previous example)
4. Determine if two lines are perpendicular 5x+2y-11=0 and 2x-5y+11=0
(Next example)





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