How do you find the area of a triangle using the Matrix?

Table of Contents

The legs of the three triangles can be found by simple subtraction of coordinates and then used to find the area since the area of a triangle is one-half the base times the height. Area of triangle A = 3 ( 3 ) / 2 = 9/2.

What is the formula to find area of a triangle using determinants?

The area of a triangle in determinant form can be determined using the formula (1/2) [x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)], where A(x1, y1), B(x2, y2), and C(x3, y3) are the vertices of the triangle ABC.

How do you find the vertices of a triangle given the equation?

how do you find the coordinates of the vertices of the triangle with the sides determined by the graphs of the following equations:4x+3y+1=0,4x-3y-17=0,4x-9y+13=0? x = 2. Substitute x = 2 into equation 1 to find y = -3 and hence one vertex is (2, -3). Find the intersection of lines 2 and 3 and then lines 1 and 3.

What is triangle in determinant?

Area of a Triangle Using Determinants. Imagine a triangle with vertices at (x1,y1), (x2,y2), and (x3,y3). If the triangle was a right-angled triangle, it would be pretty easy to compute the area of a triangle by finding one-half the product of the base and the height (area of triangle formula).

How do you find area of a triangle with coordinates?

The formula of the area of triangle in coordinate geometry is: A = (1/2)|x1 1 (y2 2 − y3 3 ) + x2 2 (y3 3 − y1 1 ) + x3 3 (y1 1 − y2 2 )|, where (x1 1 ,y1 1 ), (x2 2 ,y2 2 ), and (x3 3 ,y3 3 ) are the vertices of triangle.

What is area of triangle in coordinate geometry?

A = (1/2) [x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3(y1 – y2)] Special Case: If one of the vertices of the triangle is the origin, then the area of the triangle can be calculated using the below formula. Area of a triangle with vertices are (0,0), P(a, b), and Q(c, d) is.

How do you find the determinant of an equation?

How To

Evaluate the determinant D, using the coefficients of the variables.
Evaluate the determinant. D x . D x .
Evaluate the determinant. D y . D y .
Find x and y. x = D x D , x = D x D , y = D y D y = D y D.
Write the solution as an ordered pair.
Check that the ordered pair is a solution to both original equations.

How to find the area of a triangle with vertices?

Example: Find area of triangle whose vertices are (1, 1), (2, 3) and (4, 5) Because, Area cannot be negative. We only consider the numerical value of answer. Therefore, area of triangle = 1 sq units. This formula only works for the 1st quadrant of the coordinate system.

Can you find the area of a triangle using determinants?

However, when the triangle is not a right-angled triangle there are multiple different ways to do so. It turns out that the area of triangle formula can also be found using determinants.

How do you find the area of a collinear triangle?

From the area of triangle formula, and s ince the area is equal to zero, (p1,q1), (p2,q2), (p3,q3) are collinear. Question 2: Explain the formula of finding the area of triangle? Answer: In order to find the area of a triangle, one must multiply the base by the height. Afterward, one must divide it by 2.

Can the area of a triangle be negative?

The area of a triangle, after all, can’t be negative. Learn more about Properties of Determinants here. Let’s add the areas of the three outside triangles together. Now, to subtract the areas of the three triangles from the area of the rectangle.