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11. For two lines, find Angle, intersection point and determine if parallel or perpendicular lines example ( Enter your problem )
( 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





This material is intended as a summary. Use your textbook for detail explanation.
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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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