Question

find the area of a triangle formed by the lines 2x+y-3=0 , x+4y-5=0 , 3x+5y-1=0​

Answer 1

Answer:

The required answer is $\frac{7}{2}$

Step-by-step explanation:

Matrix: a group of numbers that have been arranged in a rectangular array using rows and columns.

Co-factors of matrix: a cofactor is used to get the adjoined inverse of the matrix. The Cofactor is the result of subtracting the column and row of a particular element from a matrix, which is just a rectangular or square-shaped numerical grid.

Given: the lines $2x+y-3=0 , x+4y-5=0 , 3x+5y-1=0$

To find: the area of a triangle.

We have

The lines are $2x+y-3=0 , x+4y-5=0 , 3x+5y-1=0$

The lines in the form of matrix.

$\left[\begin{array}{lll}2 & 1 & -3 \\1 & 4 & -5\\3 & 5 & -1 \end{array}\right]$

The cofactors of column $3$ are $-7, -7, 7$

$=(-3)(-7)+(-5)(-7)+(-1)7=49$

Area of the triangle= $\frac{\Delta^{2}}{2(-7)(-7)7}$

#SPJ3