Home > Geometry calculators > Coordinate Geometry > Find the area of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7)


Method and examples
Coordinate Geometry
 
Method  

1.1 Distance, Slope of two points
1. Find distance between the points `A(7,8)` and `B(1,0)`
2. Find slope of the line joining 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(2,5),B(8,5)``,C(5,10.196152)` are vertices of an equilateral triangle (ABC)
  5. `A(2,2),B(-2,4)``,C(2,6)` are vertices of an isosceless triangle (ABC)
  6. `A(0,0),B(0,3)``,C(4,0)` are vertices of a right angle triangle (ABC)
  7. `A(-2,-2),B(-1,2)``,C(3,1)` are vertices of a right angle triangle (ABC)
  8. `A(-3,2),B(1,2)``,C(-3,5)` are vertices of a right angle 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 = : ,
  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

 
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