Expand` |( 9, 1), (2, 0)|`

Options

A. 0
B. 1
C. -2
D. 3

Answer

To expand the determinant given by the matrix formed by the points (9, 1) and (2, 0), we will represent it in a 2x2 matrix format and calculate the determinant step by step.

### Step-by-Step Solution:

1. **Set Up the Matrix**:
We can represent the points (9, 1) and (2, 0) in a matrix format. The matrix will look like this:
\[ \Delta = \begin{bmatrix} 9 & 1 \\ 2 & 0 \end{bmatrix} \]

2. **Calculate the Determinant**:
The formula for the determinant of a 2x2 matrix \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\) is given by:
\[ \text{det} = ad - bc \]
For our matrix \(\Delta\):
- \(a = 9\)
- \(b = 1\)
- \(c = 2\)
- \(d = 0\)

Plugging in these values, we get:
\[ \text{det}(\Delta) = (9 \times 0) - (1 \times 2) \]

3. **Perform the Multiplication**:
Calculate the products:
\[ 9 \times 0 = 0 \]
\[ 1 \times 2 = 2 \]

4. **Subtract the Products**:
Now, subtract the second product from the first:
\[ 0 - 2 = -2 \]

5. **Conclusion**:
Therefore, the value of the determinant is:
\[ \text{det}(\Delta) = -2 \]

### Final Answer:
The expansion of the determinant \(|(9, 1), (2, 0)|\) is \(-2\).