How do you find the area of a triangle using the determinant of a matrix, only working backwards?

Find x, such that the triangle has an area of 4.

(-5, 1), (0, 2), (-2, x)

Can someone please help me solve for x using a graphing calculator?
Thanks!

I hope you’ll understand what i’m going` to write (i’m from Romania, in the last year of high school)
First of all, I would note the determinant of the matrix with D and the area with A , to simplify our work.
The formula of the area is : A=1/2 * | D |
the determinant looks like that :
-5 1 1
0 2 1
-2 x 1
now, we’ll solve the determinant with the triangle’s formula =>
D= -10 + 0 -2 + 4 + 5x + 0 = -12 + 4 + 5x = 5x – 8
We know that A = 4 => 1/2 * | D | = 4 => | D | = 8 => 5x – 8 = 8 =>
x = 16/5
hope it will help you in some way

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One Response to “How do you find the area of a triangle using the determinant of a matrix, only working backwards?”

Catalina_romania on March 5th, 2010 at 2:28 am

I hope you’ll understand what i’m going` to write (i’m from Romania, in the last year of high school)
First of all, I would note the determinant of the matrix with D and the area with A , to simplify our work.
The formula of the area is : A=1/2 * | D |
the determinant looks like that :
-5 1 1
0 2 1
-2 x 1
now, we’ll solve the determinant with the triangle’s formula =>
D= -10 + 0 -2 + 4 + 5x + 0 = -12 + 4 + 5x = 5x – 8
We know that A = 4 => 1/2 * | D | = 4 => | D | = 8 => 5x – 8 = 8 =>
x = 16/5
hope it will help you in some way
References :

Area List