Question

Use the he map to determine the approximate area of the Bermuda Triangle

Answer 1

Lets fill out the matrix with the corresponding coordinates.

The coordinates of Miami are (0, 0)

The coordinates of Bermuda are (900, 500)

The coordinates of San Juan, Puerto Rico are (900, -500)

Then, the matrix A is:

`\begin{bmatrix}{0} & 0{} & {1} \\ {900} & {500} & {1} \\ {900} & {-500} & {1}\end{bmatrix}`

Now to find the determinant of a 3x3 matrix, the formula is:

`\begin{gathered} X=\begin{bmatrix}{a} & {b} & {c} \\ {d} & {e} & {f} \\ {g} & {h} & {i}\end{bmatrix} \\ \det X=a\cdot\det \begin{bmatrix}{e} & {f} \\ {h} & {i}\end{bmatrix}-b\cdot\det \begin{bmatrix}{d} & {f} \\ {g} & {i}\end{bmatrix}+c\cdot\det \begin{bmatrix}{d} & {e} \\ {g} & {h}\end{bmatrix} \end{gathered}`

But since in this case, a = 0 and b = 0, the determinant of the metrix A is:

`\det A=1\cdot\det \begin{bmatrix}{900} & {500} \\ {900} & {-500}\end{bmatrix}`

Then the determinant of A is:

`\det A=1(900\cdot(-500)-500\cdot900)=-900,000`

And since the approximate area is :

`(1)/(2)|\det A|`

Then:

`\text{Area}=(1)/(2)|-900,000|=450,000mi`