Expand `|(3, 6), (5,0)|`

Answer

To expand the determinant `|(3, 6), (5, 0)|`, we will follow these steps:

### Step 1: Set up the determinant
We have a 2x2 determinant formed by the points (3, 6) and (5, 0). We can denote the determinant as follows:

\[ \Delta = \begin{vmatrix} 3 & 6 \\ 5 & 0 \end{vmatrix} \]

### Step 2: Apply the determinant formula
For a 2x2 matrix, the determinant is calculated using the formula:

\[ \text{Determinant} = ad - bc \]

where the matrix is represented as:

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

In our case, \( a = 3 \), \( b = 6 \), \( c = 5 \), and \( d = 0 \).

### Step 3: Substitute the values into the formula
Now we substitute the values into the determinant formula:

\[ \Delta = (3)(0) - (6)(5) \]

### Step 4: Calculate the products
Now we calculate each term:

\[ 3 \times 0 = 0 \]
\[ 6 \times 5 = 30 \]

### Step 5: Compute the determinant
Now we can compute the determinant:

\[ \Delta = 0 - 30 = -30 \]

### Final Answer
Thus, the value of the determinant `|(3, 6), (5, 0)|` is:

\[ \Delta = -30 \]

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