Calculate Triangle Area Using Vertex Coordinates
To find the area of a triangle given the coordinates of its vertices, we use the formula derived from the determinant method:
Area = $\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$
Let the vertices be:
- $(x_1, y_1) = (2, 4)$
- $(x_2, y_2) = (-3, -1)$
- $(x_3, y_3) = (5, 3)$
Substitute Coordinates into Formula
Substitute the coordinate values into the area formula:
Area = $\frac{1}{2} |2((-1) - 3) + (-3)(3 - 4) + 5(4 - (-1))|$
Perform Calculation
Calculate the terms inside the absolute value:
- $2((-1) - 3) = 2(-4) = -8$
- $(-3)(3 - 4) = (-3)(-1) = 3$
- $5(4 - (-1)) = 5(4 + 1) = 5(5) = 25$
Now sum these values:
Area = $\frac{1}{2} |-8 + 3 + 25|$
Area = $\frac{1}{2} |-5 + 25|$
Area = $\frac{1}{2} |20|$
Area = $\frac{1}{2} \times 20$
Final Area Result
The calculated area is:
Area = $10$ square units.
Similar Questions
- \(A(1, 2)\), \(B(a, -26)\), \(C(13, -14)\) and \(D(6, 14)\) are the vertices of a parallelogram, taken in order, find the value of \(a\).
- What would be the area of the triangle with \(A(8, 8)\), \(B(22, 8)\) and \(C(16, -10)\) as vertices?
- What would be the point which divides the line segment connecting the points \(P(10, 18), Q(5, 8)\) in the ratio \(2 : 3\) internally
- Find a point on the X axis which is equidistant from A(2, -3) and B(-2, 1)
- What is the midpoint of the line segment joining \((-2, -1)\) and \((-5, -3)\)?
- If point C is equidistant from A(5, -6) and B(7, 8), coordinate of C will be
Important Questions from Coordinate Geometry
Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
- If x² + y² - 16x + 38y + 425 = 0, then the value of x² + y² is:
- If x² + y² - 12x + 18y + 117 = 0, then the value of x² + y² is:
- A geological survey team has established three research stations forming a triangular monitoring zone. The stations are located at coordinates P(2,5), Q(8,1), and R(4,9) on a coordinate grid where each unit represents 1 kilometer. What is the area of the triangular monitoring zone?
- \(A(1, 2)\), \(B(a, -26)\), \(C(13, -14)\) and \(D(6, 14)\) are the vertices of a parallelogram, taken in order, find the value of \(a\).
