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Find the equation of the line perpendicular calculator

1 years ago
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Step 1

Choose a point that the perpendicular line will pass through.

Step 2

Rewrite the equation as .

Add to both sides of the equation.

Divide each term in by and simplify.

Cancel the common factor of .

Cancel the common factor.

Step 3

Rewrite in slope-intercept form.

The slope-intercept form is , where is the slope and is the y-intercept.

Using the slope-intercept form, the slope is .

Step 4

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

Step 5

Simplify to find the slope of the perpendicular line.

Multiply the numerator by the reciprocal of the denominator.

Step 6

Find the equation of the perpendicular line using the point-slope formula.

Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .

Simplify the equation and keep it in point-slope form.

Home > Geometry calculators > Coordinate Geometry > Determine if two lines are perpendicular calculator

Method and examples
Determine if two lines are perpendicular
 
Method  

1.1 Distance, Slope of two points

1. Find distance between the two points `A(7,8)` and `B(1,0)`

2. Find slope of the line joining two points `A(7,8)` and `B(1,0)`


A ( , ) , B ( , )
   

  1. `A(7,8),B(1,0)`
  2. `A(2,5),B(8,5)`
  3. `A(1,2),B(-3,5)`
  4. `A(-2,0),B(4,8)`
  5. `A(-2,0),B(-8,8)`
  6. `A(5,1),B(1,-2)`
  7. `A(6,4),B(-1,5)`
  8. `A(2,3),B(7,6)`
  9. `A(-3,4),B(5,-6)`
  10. `A(0,7),B(5,-2)`
  11. `A(0,0),B(-4,-6)`
  12. `A(3,5),B(6,4)`

 
1.2 Find the value of x or y

3. If distance between A(1,x) and B(-3,5) is 5, find the value of x.

Distance = , A ( , ) , B ( , )
 

  1. `distance=5`, `A(7,8),B(x,0)`
  2. `distance=5`, `A(1,x),B(-3,5)`
  3. `distance=10`, `A(x,0),B(4,8)`
  4. `distance=10`, `A(-2,x),B(-8,8)`
  5. `distance=5`, `A(5,1),B(x,-2)`
  6. `distance=6`, `A(6,x),B(-1,5)`
  7. `distance=7`, `A(2,x),B(7,6)`

 

4. If slope of A(-2,x) and B(5,-7) is -1, find the value of x.

Slope = , A ( , ) , B ( , )
 

  1. `slope=1.33`,`A(7,8),B(x,0)`
  2. `slope=-1`,`A(-2,x),B(5,-7)`
  3. `slope=3/5`,`A(2,3),B(x,6)`
  4. `slope=-5/4`,`A(-3,4),B(5,x)`
  5. `slope=-9/5`,`A(0,x),B(5,-2)`
  6. `slope=3/2`,`A(x,0),B(-4,-6)`

2. Points are Collinear or Triangle or Quadrilateral form

Find `A(0,0), B(2,2), C(0,4), D(-2,2)` are vertices of a square or not


A ( , ) , B ( , ) , C ( , ) , D ( , )
Find  
 

  1. `A(-1,-1),B(1,5)``,C(2,8)` are vertices of are collinear points (ABC)
  2. `A(0,-1),B(3,5)``,C(5,9)` are vertices of are collinear points (ABC)
  3. `A(2,8),B(1,5)``,C(0,2)` are vertices of are collinear points (ABC)
  4. `A(0,0),B(0,3)``,C(4,0)` are vertices of a right angle triangle (ABC)
  5. `A(-2,-2),B(-1,2)``,C(3,1)` are vertices of a right angle triangle (ABC)
  6. `A(-3,2),B(1,2)``,C(-3,5)` are vertices of a right angle triangle (ABC)
  7. `A(2,5),B(8,5)``,C(5,10.196152)` are vertices of an equilateral triangle (ABC)
  8. `A(2,2),B(-2,4)``,C(2,6)` are vertices of an isosceless triangle (ABC)
  9. `A(0,0),B(2,0)``,C(-4,0)``,D(-2,0)` are vertices of are collinear points (ABCD)
  10. `A(2,3),B(7,4)``,C(8,7)``,D(3,6)` are vertices of a parallelogram (ABCD)
  11. `A(1,5),B(1,4)``,C(-1,3)``,D(-1,4)` are vertices of a parallelogram (ABCD)
  12. `A(1,-1),B(-2,2)``,C(4,8)``,D(7,5)` are vertices of a rectangle (ABCD)
  13. `A(0,-4),B(6,2)``,C(3,5)``,D(-3,-1)` are vertices of a rectangle (ABCD)
  14. `A(3,0),B(4,5)``,C(-1,4)``,D(-2,-1)` are vertices of a rhombus (ABCD)
  15. `A(3,2),B(5,4)``,C(3,6)``,D(1,4)` are vertices of a square (ABCD)
  16. `A(0,0),B(2,2)``,C(0,4)``,D(-2,2)` are vertices of a square (ABCD)

3. Find Ratio

1. Find ratio of line joining A(5,12) and B(2,9) is divided by a point P(3,10)

A ( , ) , B ( , ) , P ( , )
 

  1. `A(1,-3),B(3,5),P(6,17)`
  2. `A(2,8),B(6,14),P(12,23)`
  3. `A(5,12),B(2,9),P(3,10)`
  4. `A(5,13),B(1,4),P(17/5,47/5)`

 

2. Find a point which divides the line joining A(-4,1) and B(17,10) in the ratio 1:2

A ( , ) , B ( , ) , ratio = : , Externally
 

  1. `A(5,13),B(1,4),m:n=2:3`
  2. `A(-4,1),B(17,10),m:n=1:2`
  3. `A(5,12),B(2,9),m:n=2:1`
  4. `A(2,8),B(6,14),m:n=5:3` Externally
  5. `A(1,-3),B(3,5),m:n=5:3` Externally

 

3. Find the ratio in which the x-axis divides the join of `A(2,1)` and `B(7,6)`? Also find the coordinates of the point of intersection.

A ( , ) , B ( , ) , divided by
 

  1. `A(2,1),B(7,6)` divided by x-axis
  2. `A(2,-4),B(-3,6)` divided by x-axis
  3. `A(2,-4),B(-3,6)` divided by y-axis

 

4. Find the ratio in which the point `P(x,4)` divides the join of `A(2,1)` and `B(7,6)`? Also find the value of `x`.

P ( , ) , A ( , ) , B ( , ) ,
 

  1. `P(x,4),A(2,1),B(7,6)`
  2. `P(x,0),A(2,-4),B(-3,6)`
  3. `P(0,y),A(2,-4),B(-3,6)`

4. Find Midpoint or Trisection points or equidistant points on X-Y axis

1. Find the midpoint of line joining points `A(-2,3)` and `B(5,4)`

2. Find the trisection points of line joining points `A(-2,3)` and `B(5,4)`

3. Find the point on the x-axis which is equidistant from `A(-2,3)` and `B(5,4)`

4. Find the point on the y-axis which is equidistant from `A(-2,3)` and `B(5,4)`


A ( , ) , B ( , )
 
       

  1. `A(-4,1),B(17,10)`
  2. `A(-2,3),B(5,4)`
  3. `A(-3,4),B(5,-6)`
  4. `A(0,7),B(5,-2)`
  5. `A(0,0),B(-4,-6)`
  6. `A(3,5),B(6,4)`

5. Find Centroid, Circumcenter, Area of a triangle

1. Find the centroid of a triangle whose vertices are `A(4,1),B(-2,-3),C(6,7)`

2. Find the circumcentre of a triangle whose vertices are `A(4,1),B(-2,-3),C(6,7)`

3. Find the area of a triangle whose vertices are `A(4,1),B(-2,-3),C(6,7)`

4. Find `A(4,1),B(-2,-3),C(6,7)` are collinear points or not (using area finding method)


A ( , ) , B ( , ) , C ( , )
 
       

  1. `A(2,5),B(4,9),C(6,4)`
  2. `A(-1,-1),B(1,5),C(2,8)`
  3. `A(-3,2),B(1,2),C(-3,5)`
  4. `A(0,-1),B(3,5),C(5,9)`
  5. `A(4,1),B(-2,-3),C(6,7)`

6. Find the equation of a line using slope, point, X-intercept, Y-intercept

1. Find the equation of a line passing through point `A(5,4)` and having slope `1/2`

A ( , ) ; Slope :
 

  1. slope`=2`,`A(0,3)`
  2. slope`=1/4`,`A(0,0)`
  3. slope`=1/2`,`A(5,4)`

 

2. Find the equation of a line passing through two points `A(3,5)` and `B(6,4)`

A ( , ) , B ( , )
 

  1. `A(7,8),B(1,0)`
  2. `A(6,4),B(-1,5)`
  3. `A(2,3),B(7,6)`
  4. `A(-3,4),B(5,-6)`
  5. `A(0,7),B(5,-2)`
  6. `A(0,0),B(-4,-6)`
  7. `A(3,5),B(6,4)`

 

3. Find the equation of a line having slope = 2 and Y-intercept = 3

Slope : ; Y-intercept :
 

  1. slope`=1/2`,Y-intercept`=5`
  2. slope`=1/4`,Y-intercept`=0`
  3. slope`=2`,Y-intercept`=3`

 

4. Find the equation of a line having X-intercept = 3 and Y-intercept = -5

X-intercept : ; Y-intercept :
 

  1. X-intercept`=2`,Y-intercept`=-2`
  2. X-intercept`=-5/3`,Y-intercept`=5`
  3. X-intercept`=-3/5`,Y-intercept`=-3/2`
  4. X-intercept`=3`,Y-intercept`=-5`

7. Find Slope, X-intercept, Y-intercept of a line

1. Find Slope and Y-intercept of a line 7y-4x+9=0

2. Find X-intercept and Y-intercept of a line 7y-4x+9=0

3. Find Slope, X-intercept and Y-intercept of a line 7y-4x+9=0


Line :
     

  1. Line`:2x+3y+4=0`
  2. Line`:3x+6y-8=0`
  3. Line`:4x+5y+7=0`
  4. Line`:3x-2y-12=0`
  5. Line`:7y-4x+9=0`
  6. Line`:5x+2y-11=0`
  7. Line`:3x-y+11=0`
  8. Line`:4x-3y+2=0`

 

4. Find Slope, X-intercept and Y-intercept of the line joining the points `A(3,-5)` and `B(-7,9)`

A ( , ) , B ( , )
 

  1. `A(7,8),B(1,0)`
  2. `A(6,4),B(-1,5)`
  3. `A(2,3),B(7,6)`
  4. `A(-3,4),B(5,-6)`
  5. `A(0,7),B(5,-2)`
  6. `A(0,0),B(-4,-6)`
  7. `A(3,5),B(6,4)`
  8. `A(3,-5),B(-7,9)`

 

8. Find the equation of a line passing through point of intersection of two lines and slope or a point

1. Find the equation of a line passing through point of intersection of lines `2x+3y+4=0` and `3x+6y-8=0` and having slope = 2


Line-1 : , Line-2 : , Slope :
 

  1. Line-1`:x-4y+18=0`,Line-2`:x+y-12=0`,slope`=2`
  2. Line-1`:2x+3y+4=0`,Line-2`:3x+6y-8=0`,slope`=2`
  3. Line-1`:x=3y`,Line-2`:3x=2y+7`,slope`=-1/2`

 

2. Find the equation of a line passing through point of intersection of lines `4x+5y+7=0` and `3x-2y-12=0` and point `A(3,1)`


Line-1 : , Line-2 : , A ( , )
 

  1. Line-1`:x+y+1=0`,Line-2`:3x+y-5=0`,`A(1,-3)`
  2. Line-1`:4x+5y+7=0`,Line-2`:3x-2y-12=0`,`A(3,1)`

9. Find the equation of a line passing through a point and parallel or perpendicular to Line-2

1. Find the equation of a line passing through point `A(5,5)` and parallel to the line `2x+3y+4=0`

2. Find the equation of a line passing through point `A(5,5)` and perpendicular to the line `2x+3y+4=0`


A ( , ) , Line-2 :
   

  1. `A(5,7)`,Line`:2x+3y+5=0`
  2. `A(4,2)`,Line`:3x-2y=5`
  3. `A(5,5)`,Line`:2x+3y+4=0`

 

3. Find the equation of a line passing through point `A(5,5)` and parallel to the line passing `B(1,-2)` and `C(-5,2)`

4. Find the equation of a line passing through point `A(5,5)` and perpendicular to the line passing `B(1,-2)` and `C(-5,2)`


A ( , ) , B ( , ) , C ( , ) ,
   

  1. `A(5,7),B(-1,-1),C(-4,1)`
  2. `A(4,2),B(1,-1),C(3,2)`
  3. `A(5,5),B(1,-2),C(-5,2)`

10. Find the equation of a line passing through point of intersection of Line-1, Line-2 and parallel or perpendicular to Line-3

1. Find the equation of a line passing through point of intersection of the lines `5x+2y-11=0` and `3x-y+11=0` and it is parallel to `4x-3y+2=0`

2. Find the equation of a line passing through point of intersection of the lines `5x+2y-11=0` and `3x-y+11=0` and it is perpendicular to `4x-3y+2=0`


Line-1 : , Line-2 : , Line-3 :
 
   

  1. Line-1`:x-y=1`,Line-2`:2x-3y+1=0`,Line-3`:5x+6y=7`
  2. Line-1`:x-2y+15=0`,Line-2`:3x+y-4=0`,Line-3`:2x-3y+7=0`
  3. Line-1`:5x+2y-11=0`,Line-2`:3x-y+11=0`,Line-3`:4x-3y+2=0`

11. For two lines, find Angle, intersection point and determine if parallel or perpendicular lines

1. Find angle between two lines `5x+2y-11=0` and `3x-y+11=0`

2. Find intersection point of `5x+2y-11=0` and `3x-y+11=0`

3. is parallel lines `2x+3y=11` and `4x+6y=5`

4. is perpendicular lines `2x+3y=11` and `3x-2y=5`


Line-1 : , Line-2 :
       

  1. Line-1`:x-y=1`,Line-2`:2x-3y+1=0`
  2. Line-1`:x-2y+15=0`,Line-2`:3x+y-4=0`
  3. Line-1`:5x+2y-11=0`,Line-2`:3x-y+11=0`

12. Reflection of points about x-axis, y-axis, origin

Find Reflection of pointsA(0,0),B(2,2),C(0,4),D(-2,2) and Reflection about X,Y,O


A ( , ) , B ( , ) , C ( , ) , D ( , ) , Reflection =
 

  1. `A(-2,-2),B(-1,2),C(3,1)` and Reflection about X
  2. `A(2,3),B(7,4),C(8,7),D(3,6)` and Reflection about Y
  3. `A(1,-1),B(-2,2),C(4,8),D(7,5)` and Reflection about O
  4. `A(3,0),B(4,5),C(-1,4),D(-2,-1)` and Reflection about X,Y
  5. `A(3,2),B(5,4),C(3,6),D(1,4)` and Reflection about Y,X
  6. `A(-1,-1),B(1,5),C(2,8)` and Reflection about X
  7. `A(-3,2),B(1,2),C(-3,5)` and Reflection about Y
  8. `A(0,-1),B(3,5),C(5,9)` and Reflection about X
  9. `A(2,8),B(1,5),C(0,2)` and Reflection about Y
  10. `A(0,0),B(2,2),C(0,4),D(-2,2)` and Reflection about X,Y,O

 

Find the equation of the line perpendicular calculator
Find the equation of the line perpendicular calculator
Find the equation of the line perpendicular calculator
Find the equation of the line perpendicular calculator
Find the equation of the line perpendicular calculator
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find equation line perpendicular calculator Find perpendicular line

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