Expand` |(2,0), (5, 7)|`

Answer

To expand the determinant given by the points (2, 0) and (5, 7), we can follow these steps:

### Step 1: Define the Determinant
Let \( A \) be the determinant formed by the points (2, 0) and (5, 7). We can express this as:
\[ A = \begin{vmatrix} 2 & 0 \\ 5 & 7 \end{vmatrix} \]

### Step 2: Calculate the Determinant
The formula for the determinant of a 2x2 matrix is given by:
\[ \text{det}(A) = ad - bc \]
where \( a, b, c, d \) are the elements of the matrix:
\[ A = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = \begin{vmatrix} 2 & 0 \\ 5 & 7 \end{vmatrix} \]
Here, \( a = 2 \), \( b = 0 \), \( c = 5 \), and \( d = 7 \).

Substituting these values into the determinant formula:
\[ \text{det}(A) = (2)(7) - (5)(0) \]

### Step 3: Simplify the Expression
Now, calculate the values:
\[ \text{det}(A) = 14 - 0 = 14 \]

### Final Result
Thus, the value of the determinant is:
\[ \text{det}(A) = 14 \]

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