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Home > Geometry calculators > Coordinate Geometry > Equation of line passing through a given point and perpendicular to given line calculator
Method and examples
Method  
Equation of line passing through a given point and perpendicular to given line
1. Distance, Slope of two points
 
1. Find the distance between the points `A(5,-8)` and `B(-7,-3)`
2. Find the slope of the line joining points `A(4,-8)` and `B(5,-2)`

A ( , ) , B ( , )
    `
  1. `A(5,-8),B(-7,-3)`
  2. `A(7,-4),B(-5,1)`
  3. `A(-6,-4),B(9,-12)`
  4. `A(1,-3),B(4,-6)`
  5. `A(-5,7),B(-1,3)`
  6. `A(-8,6),B(2,0)`
  7. `A(0,0),B(7,4)`
Find the value of x or y
 
3. If distance between the points (5,3) and (x,-1) is 5, then find the value of x.
A ( , ) , B ( , ) , Distance =
 
  1. `A(5,3),B(x,-1)`, distance `=5`
  2. `A(x,-1),B(3,2)`, distance `=5`
  3. `A(x,2),B(3,-6)`, distance `=10`
  4. `A(x,1),B(-1,5)`, distance `=5`
  5. `A(x,7),B(1,15)`, distance `=10`
  6. `A(1,x),B(-3,5)`, distance `=5`
  7. `A(x,0),B(4,8)`, distance `=10`
 
4. If slope of the line joining points `A(x,0), B(-3,-2)` is `2/7`, find the value of `x`
A ( , ) , B ( , ) , Slope =
 
  1. `A(x,0),B(-3,-2)`, slope `=2/7`
  2. `A(2,x),B(-3,7)`, slope `=1`
  3. `A(x,5),B(-1,2)`, slope `=3/4`
  4. `A(2,5),B(x,3)`, slope `=2`
  5. `A(x,2),B(6,-8)`, slope `=-5/4`
  6. `A(-2,x),B(5,-7)`, slope `=-1`
  7. `A(2,3),B(x,6)`, slope `=3/5`
  8. `A(-3,4),B(5,x)`, slope `=-5/4`
  9. `A(0,x),B(5,-2)`, slope `=-9/5`
2. Points are Collinear or Triangle or Quadrilateral form
 
Show that the points are the vertices of  
Find `A(0,0), B(2,2), C(0,4), D(-2,2)` are vertices of a square or not

A ( , ) , B ( , ) , C ( , ) , D ( , )
 
  1. `A(1,5),B(2,3),C(-2,-11)` are collinear points
  2. `A(1,-3),B(2,-5),C(-4,7)` are collinear points
  3. `A(-1,-1),B(1,5),C(2,8)` are collinear points
  4. `A(0,-1),B(3,5),C(5,9)` are collinear points
  5. `A(2,8),B(1,5),C(0,2)` are collinear points
  6. `A(-1,-1),B(1,5),C(2,8)` are collinear points
  7. `A(0,-1),B(3,5),C(5,9)` are collinear points
  8. `A(2,8),B(1,5),C(0,2)` are collinear points
  9. `A(0,0),B(0,3),C(4,0)` are vertices of a right angle triangle
  10. `A(-2,-2),B(-1,2),C(3,1)` are vertices of a right angle triangle
  11. `A(-3,2),B(1,2),C(-3,5)` are vertices of a right angle triangle
  12. `A(2,5),B(8,5),C(5,10.196152)` are vertices of an equilateral triangle
  13. `A(2,2),B(-2,4),C(2,6)` are vertices of an isosceles triangle
  14. `A(0,0),B(2,0),C(-4,0),D(-2,0)` are collinear points
  15. `A(3,2),B(5,4),C(3,6),D(1,4)` are vertices of a square
  16. `A(0,0),B(2,2),C(0,4),D(-2,2)` are vertices of a square
  17. `A(1,-1),B(-2,2),C(4,8),D(7,5)` are vertices of a rectangle
  18. `A(0,-4),B(6,2),C(3,5),D(-3,-1)` are vertices of a rectangle
  19. `A(3,0),B(4,5),C(-1,4),D(-2,-1)` are vertices of a rhombus
  20. `A(2,3),B(7,4),C(8,7),D(3,6)` are vertices of a parallelogram
  21. `A(1,5),B(1,4),C(-1,3),D(-1,4)` are vertices of a parallelogram
3. Find Ratio of line joining AB and is divided by P
 
1. Find the ratio in which the point P(3/4, 5/12) divides the line segment joining the points A(1/2, 3/2) and B(2, -5)
P ( , ) , A ( , ) , B ( , )
 
  1. `P(3/4,5/12),A(1/2,3/2),B(2,-5)`
  2. `P(-1,6),A(3,10),B(6,-8)`
  3. `P(-2,3),A(-3,5),B(4,-9)`
  4. `P(3,10),A(5,12),B(2,9)`
  5. `P(6,17),A(1,-3),B(3,5)`
  6. `P(12,23),A(2,8),B(6,14)`
  7. `P(3,10),A(5,12),B(2,9)`
  8. `P(6,17),A(1,-3),B(3,5)`
  9. `P(12,23),A(2,8),B(6,14)`
  10. `P(17/5,47/5),A(5,13),B(1,4)`
2. Write down the co-ordinates of the point P that divides the line joining A(-4,1) and B(17,10) in the ratio 1:2
A ( , ) , B ( , ) , ratio = : ,
 
  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. In what ratio does the x-axis divide the join of `A(2,-3)` and `B(5,6)`? Also find the coordinates of the point of intersection.
A ( , ) , B ( , ) , divided by
 
  1. `A(2,-3),B(5,6)` divided by x-axis
  2. `A(1,2),B(2,3)` divided by x-axis
  3. `A(5,-6),B(-1,-4)` divided by y-axis
  4. `A(-2,1),B(4,5)` divided by y-axis
  5. `A(2,1),B(7,6)` divided by x-axis
  6. `A(2,-4),B(-3,6)` divided by y-axis
4. Find the ratio in which the point `P(x,4)` divides the line segment joining the points `A(2,1)` and `B(7,6)`? Also find the value of `x`.
P ( , ) , A ( , ) , B ( , ) ,
 
  1. `P(x,2),A(12,5),B(4,-3)`
  2. `P(11,y),A(15,5),B(9,20)`
  3. `P(-3,y),A(-5,-4),B(-2,3)`
  4. `P(-4,y),A(-6,10),B(3,-8)`
  5. `P(x,4),A(2,1),B(7,6)`
  6. `P(x,0),A(2,-4),B(-3,6)`
  7. `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 coordinates of the midpoint of the line segment joining the points `A(-5,4)` and `B(7,-8)`
2. Find the trisectional points of line joining `A(-3,-5)` and `B(-6,-8)`
3. Find the point on the x-axis which is equidistant from `A(5,4)` and `B(-2,3)`
4. Find the point on the y-axis which is equidistant from `A(6,5)` and `B(-4,3)`

A ( , ) , B ( , )
 
       
  1. `A(-5,4),B(7,-8)`
  2. `A(2,1),B(1,-3)`
  3. `A(2,1),B(5,3)`
  4. `A(3,-5),B(1,1)`
  5. `A(1,-1),B(-5,-3)`
  6. `A(-7,-3),B(5,3)`
5. Find Centroid, Circumcenter, Area of a triangle
 
1. Find the centroid of a triangle whose vertices are `A(4,-6),B(3,-2),C(5,2)`
2. Find the circumcentre of a triangle whose vertices are `A(-2,-3),B(-1,0),C(7,-6)`
3. Using determinants, find the area of the triangle with vertices are `A(-3,5),B(3,-6),C(7, 2)`
4. Using determinants show that the following points are collinear `A(2,3),B(-1,-2),C(5,8)`

A ( , ) , B ( , ) , C ( , )
 
       
  1. `A(4,-6),B(3,-2),C(5,2)`
  2. `A(3,-5),B(-7,4),C(10,-2)`
  3. `A(4,-8),B(-9,7),C(8,13)`
  4. `A(3,-7),B(-8,6),C(5,10)`
  5. `A(2,4),B(6,4),C(2,0)`
6. Find the equation of a line using slope, point, X-intercept, Y-intercept
 
1. Find the equation of a straight line passing through `A(-4,5)` and having slope `-2/3`
A ( , ) , Slope :
 
  1. `A(-4,5)`,slope`=-2/3`
  2. `A(4,5)`,slope`=1`
  3. `A(-2,3)`,slope`=-4`
  4. `A(-1,2)`,slope`=-5/4`
  5. `A(0,3)`,slope`=2`
  6. `A(0,0)`,slope`=1/4`
  7. `A(5,4)`,slope`=1/2`
2. Find the equation of a straight line passing through the points `A(7,5)` and `B(-9,5)`
A ( , ) , B ( , )
 
  1. `A(7,5),B(-9,5)`
  2. `A(-1,1),B(2,-4)`
  3. `A(-5,-6),B(3,10)`
  4. `A(3,-5),B(4,-8)`
  5. `A(-1,-4),B(3,0)`
  6. `A(7,8),B(1,0)`
  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)`
3. Find the equation of a line having slope `1/2` and y-intercept `-3`
Slope : ; Y-intercept :
 
  1. slope`=1/2`,Y-intercept`=-3`
  2. slope`=-1/2`,Y-intercept`=3`
  3. slope`=2`,Y-intercept`=-3`
  4. slope`=2`,Y-intercept`=3/2`
  5. slope`=1/2`,Y-intercept`=5`
  6. slope`=1/4`,Y-intercept`=0`
  7. slope`=2`,Y-intercept`=3`
4. Find the equation of a line whose x-intercept is 5 and y-intercept is 2
X-intercept : ; Y-intercept :
 
  1. X-intercept`=5`,Y-intercept`=2`
  2. X-intercept`=3`,Y-intercept`=-2`
  3. X-intercept`=-2/7`,Y-intercept`=3/5`
  4. X-intercept`=6`,Y-intercept`=-4`
  5. X-intercept`=2`,Y-intercept`=-2`
  6. X-intercept`=-5/3`,Y-intercept`=5`
  7. X-intercept`=-3/5`,Y-intercept`=-3/2`
  8. X-intercept`=3`,Y-intercept`=-5`
7. Find Slope, X-intercept, Y-intercept of a line
 
1. Find the slope and y-intercept of the line 2x+3y=4
2. Find x-intercept and y-intercept of the line 2x+3y=4
3. Find the slope, x-intercept and y-intercept of the line 2x+3y=4

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

Click here to Find Line using Slope, X-intercept, Y-intercept Calculator
4. Find the slope, x-intercept and y-intercept of the line joining the points `A(1,3)` and `B(3,5)`
A ( , ) , B ( , )
 
  1. `A(1,3),B(3,5)`
  2. `A(4,-8),B(5,-2)`
  3. `A(7,1),B(8,9)`
  4. `A(4,8),B(5,5)`
  5. `A(7,8),B(1,0)`
  6. `A(6,4),B(-1,5)`
  7. `A(2,3),B(7,6)`
  8. `A(-3,4),B(5,-6)`
  9. `A(0,7),B(5,-2)`
  10. `A(0,0),B(-4,-6)`
  11. `A(3,5),B(6,4)`
  12. `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 the point of intersection of lines `3x+4y=7` and `x-y+2=0` and having slope 5
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`
  4. Line-1`:x-4y+18=0`,Line-2`:x+y-12=0`,slope`=2`
  5. Line-1`:2x+3y+4=0`,Line-2`:3x+6y-8=0`,slope`=2`
  6. Line-1`:x=3y`,Line-2`:3x=2y+7`,slope`=-1/2`
2. Find the equation of a line passing through the 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 the line passing through the point `A(5,4)` and parallel to the line `2x+3y+7=0`
2. Find the equation of the line passing through the point `A(1,1)` and perpendicular to the line `2x-3y+2=0`

A ( , ) , Line-2 :
   
  1. `A(1,1)`,Line`:2x-3y+2=0`
  2. `A(0,0)`,Line`:7x-3y+4=0`
  3. `A(3,2)`,Line`:y=5x+2`
  4. `A(-1,1)`,Line`:2x+3y+4=0`
3. Find the equation of the line passing through the point `A(1,3)` and parallel to line passing through the points `B(3,-5)` and `C(-6,1)`
4. Find the equation of the line passing through the point `A(5,5)` and perpendicular to the line passing through the points `B(1,-2)` and `C(-5,2)`

A ( , ) , B ( , ) , C ( , ) ,
   
  1. `A(1,3),B(3,-5),C(-6,1)`
  2. `A(4,-5),B(3,7),C(-2,4)`
  3. `A(-1,3),B(0,2),C(4,5)`
  4. `A(2,-3),B(1,2),C(-1,5)`
  5. `A(4,2),B(1,-1),C(3,2)`
  6. `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 the line passing through the point of intersection of the lines `x-y=1` and `2x-3y+1=0` and parallel to the line `3x+4y=12`
2. Find the equation of the line passing through the point of intersection of the lines `2x+3y=1` and `3x+4y=6` and perpendicular to the line `5x-2y=7`
 
Line-1 :
Line-2 :
Line-3 :
   
  1. Line-1`:x-y=1`,Line-2`:2x-3y+1=0`,Line-3`:3x+4y=12`
  2. Line-1`:x-y=1`,Line-2`:2x-3y+1=0`,Line-3`:5x+6y=7`
  3. Line-1`:x-2y+15=0`,Line-2`:3x+y-4=0`,Line-3`:2x-3y+7=0`
  4. Line-1`:5x+2y-11=0`,Line-2`:3x-y+11=0`,Line-3`:4x-3y+2=0`
11. Find Angle, intersection point and determine if parallel or perpendicular lines
 
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
 
Line-1 :
Line-2 :
       
  1. Line-1`:x+3y+1=0`,Line-2`:2x-y+4=0`
  2. Line-1`:3x+2y+4=0`,Line-2`:2x-3y-7=0`
  3. Line-1`:2x+3y+5=0`,Line-2`:x-2y-4=0`
  4. Line-1`:3x-y+4=0`,Line-2`:2x+y=3`
  5. Line-1`:2x-y+3=0`,Line-2`:x-3y+7=0`
12. Reflection of points about x-axis, y-axis, origin
 
Find Reflection of points A(0,0),B(2,2),C(0,4),D(-2,2) and Reflection about X,Y,O

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

Reflection about
 
  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 y=x
  7. `A(-3,2),B(1,2),C(-3,5)` and Reflection about y=-x
  8. `A(0,-1),B(3,5),C(5,9)` and Reflection about x=2
  9. `A(2,8),B(1,5),C(0,2)` and Reflection about y=2
  10. `A(0,0),B(2,2),C(0,4),D(-2,2)` and Reflection about x+3y-7=0
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