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Home > Geometry calculators > Coordinate Geometry > Use determinants to show that the following points are collinear calculator
Method and examples
Method  
 
Collinear points using determinants
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(2,3),B(-1,-2),C(5,8)`
  2. `A(8,1),B(3,-4),C(2,-5)`
  3. `A(3,-2),B(5,2),C(8,8)`
  4. `A(3,8),B(-4,2),C(10,14)`
  5. `A(1,5),B(2,3),C(2,11)`
  6. `A(2,5),B(5,7),C(8,9)`
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(5,4)`,Line`:2x+3y+7=0`
  2. `A(1,1)`,Line`:2x-3y+2=0`
  3. `A(2,3)`,Line`:2x-3y+8=0`
  4. `A(2,-5)`,Line`:2x-3y-7=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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