Area Of Triangle With Vertices Calculator

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Home > Geometry calculators > Coordinate Geometry > Area of triangle with vertices calculator

Method and examples

Method 1. Distance, Slope from two points 2. Points (3 or 4) are Collinear or Triangle or Quadrilateral form 3. Find Ratio of line joining AB and is divided by P 4. Midpoint or Trisection points or equidistant points on X-Y axis 5. Find Centroid, Circumcenter, Area of a triangle 6. Find equation of a line using slope, point, X-intercept, Y-intercept 7. Find Slope, X-intercept, Y-intercept of a line 8. Find line passing through intersection point of two lines and slope or a point 9. Find line passing through a point and parallel or perpendicular to Line-2 10. Find line passing through intersection point Line-1,Line-2 parallel to Line-3 11. Find Angle, intersection point and determine if parallel lines 12. Reflection of points about x-axis, y-axis, origin

Area of triangle by coordinates

Using determinants, find the area of the triangle with vertices are A(-3,5),B(3,-6),C(7, 2)

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 ( , )

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

Mode = Decimal Fraction

Decimal Place = 0 1 2 3 4 5 6 7 8 9 10

SolutionMethods

Solution

Solution provided by AtoZmath.com

Area of triangle by coordinates calculator

1. Using determinants, find the area of the triangle with vertices are `A(-3,5),B(3,-6),C(7,2)`

2. Using determinants, find the area of the triangle with vertices are `A(1,4),B(2,3),C(-5,-3)`

3. Using determinants, find the area of the triangle with vertices are `A(-2,-3),B(3,2),C(-1,-8)`

4. Using determinants, find the area of the triangle with vertices are `A(1,0),B(6,0),C(4,3)`

5. Using determinants, find the area of the triangle with vertices are `A(3,8),B(-4,2),C(5,1)`

6. Using determinants, find the area of the triangle with vertices are `A(-2,4),B(2,-6),C(5,4)`

Example1. Using determinants, find the area of the triangle with vertices are `A(-3,5),B(3,-6),C(7,2)`Solution:The given points are `A(-3,5),B(3,-6),C(7,2)``:. x_1=-3,y_1=5,x_2=3,y_2=-6,x_3=7,y_3=2`Area of a triangle `=1/2 |[x_1,y_1,1],[x_2,y_2,1],[x_2,y_2,1]|``=1/2 |[-3,5,1],[3,-6,1],[7,2,1]|``=1/2[-3 xx (-6 × 1 - 1 × 2) -5 xx (3 × 1 - 1 × 7) +1 xx (3 × 2 - (-6) × 7)]``=1/2[-3 xx (-6 -2) -5 xx (3 -7) +1 xx (6 +42)]``=1/2[-3 xx (-8) -5 xx (-4) +1 xx (48)]``=1/2[24 +20 +48]``=1/2[92]``=46`Thus, the area of triangle is `46` square units

2. Using determinants, find the area of the triangle with vertices are `A(-3,5),B(3,-6),C(7,2)`Solution:The given points are `A(-3,5),B(3,-6),C(7,2)``:. x_1=-3,y_1=5,x_2=3,y_2=-6,x_3=7,y_3=2`Area of a triangle `=1/2 |[x_1,y_1,1],[x_2,y_2,1],[x_2,y_2,1]|``=1/2 |[-3,5,1],[3,-6,1],[7,2,1]|``=1/2[-3 xx (-6 × 1 - 1 × 2) -5 xx (3 × 1 - 1 × 7) +1 xx (3 × 2 - (-6) × 7)]``=1/2[-3 xx (-6 -2) -5 xx (3 -7) +1 xx (6 +42)]``=1/2[-3 xx (-8) -5 xx (-4) +1 xx (48)]``=1/2[24 +20 +48]``=1/2[92]``=46`Thus, the area of triangle is `46` square units

3. Using determinants, find the area of the triangle with vertices are `A(-2,-3),B(3,2),C(-1,-8)`Solution:The given points are `A(-2,-3),B(3,2),C(-1,-8)``:. x_1=-2,y_1=-3,x_2=3,y_2=2,x_3=-1,y_3=-8`Area of a triangle `=1/2 |[x_1,y_1,1],[x_2,y_2,1],[x_2,y_2,1]|``=1/2 |[-2,-3,1],[3,2,1],[-1,-8,1]|``=1/2[-2 xx (2 × 1 - 1 × (-8)) +3 xx (3 × 1 - 1 × (-1)) +1 xx (3 × (-8) - 2 × (-1))]``=1/2[-2 xx (2 +8) +3 xx (3 +1) +1 xx (-24 +2)]``=1/2[-2 xx (10) +3 xx (4) +1 xx (-22)]``=1/2[-20 +12 -22]``=1/2[-30]``=-15``=15` (As area is positive)Thus, the area of triangle is `15` square units

4. Using determinants, find the area of the triangle with vertices are `A(1,0),B(6,0),C(4,3)`Solution:The given points are `A(1,0),B(6,0),C(4,3)``:. x_1=1,y_1=0,x_2=6,y_2=0,x_3=4,y_3=3`Area of a triangle `=1/2 |[x_1,y_1,1],[x_2,y_2,1],[x_2,y_2,1]|``=1/2 |[1,0,1],[6,0,1],[4,3,1]|``=1/2[1 xx (0 × 1 - 1 × 3) +0 xx (6 × 1 - 1 × 4) +1 xx (6 × 3 - 0 × 4)]``=1/2[1 xx (0 -3) +0 xx (6 -4) +1 xx (18 +0)]``=1/2[1 xx (-3) +0 xx (2) +1 xx (18)]``=1/2[-3 +0 +18]``=1/2[15]``=15/2`Thus, the area of triangle is `15/2` square units

5. Using determinants, find the area of the triangle with vertices are `A(3,8),B(-4,2),C(5,1)`Solution:The given points are `A(3,8),B(-4,2),C(5,1)``:. x_1=3,y_1=8,x_2=-4,y_2=2,x_3=5,y_3=1`Area of a triangle `=1/2 |[x_1,y_1,1],[x_2,y_2,1],[x_2,y_2,1]|``=1/2 |[3,8,1],[-4,2,1],[5,1,1]|``=1/2[3 xx (2 × 1 - 1 × 1) -8 xx (-4 × 1 - 1 × 5) +1 xx (-4 × 1 - 2 × 5)]``=1/2[3 xx (2 -1) -8 xx (-4 -5) +1 xx (-4 -10)]``=1/2[3 xx (1) -8 xx (-9) +1 xx (-14)]``=1/2[3 +72 -14]``=1/2[61]``=61/2`Thus, the area of triangle is `61/2` square units

6. Using determinants, find the area of the triangle with vertices are `A(-2,4),B(2,-6),C(5,4)`Solution:The given points are `A(-2,4),B(2,-6),C(5,4)``:. x_1=-2,y_1=4,x_2=2,y_2=-6,x_3=5,y_3=4`Area of a triangle `=1/2 |[x_1,y_1,1],[x_2,y_2,1],[x_2,y_2,1]|``=1/2 |[-2,4,1],[2,-6,1],[5,4,1]|``=1/2[-2 xx (-6 × 1 - 1 × 4) -4 xx (2 × 1 - 1 × 5) +1 xx (2 × 4 - (-6) × 5)]``=1/2[-2 xx (-6 -4) -4 xx (2 -5) +1 xx (8 +30)]``=1/2[-2 xx (-10) -4 xx (-3) +1 xx (38)]``=1/2[20 +12 +38]``=1/2[70]``=35`Thus, the area of triangle is `35` square units