Find the value of `|(-8,6),(5,4)|`

Options

A. `-62`
B. `-30`
C. `-32`
D. `-62`

Answer

To find the value of the determinant of the matrix formed by the points \((-8, 6)\) and \((5, 4)\), we can represent this as a 2x2 matrix:

\[ \begin{pmatrix} -8 & 6 \\ 5 & 4 \end{pmatrix} \]

The determinant \( |A| \) of a 2x2 matrix

\[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \]

is calculated using the formula:

\[ |A| = ad - bc \]

Here, we can identify:
- \( a = -8 \)
- \( b = 6 \)
- \( c = 5 \)
- \( d = 4 \)

Now, we can substitute these values into the determinant formula:

1. Calculate \( ad \):
\[ ad = (-8) \times 4 = -32 \]

2. Calculate \( bc \):
\[ bc = 6 \times 5 = 30 \]

3. Now, substitute these results into the determinant formula:
\[ |A| = ad - bc = -32 - 30 \]

4. Simplify the expression:
\[ |A| = -32 - 30 = -62 \]

Thus, the value of the determinant \( |(-8, 6),(5, 4)| \) is \(-62\).