If the vertices of a triangle are `(u,0),(v,8), and (0,0) then the area of the triiangle is

Options

A. `4|u|`
B. `2|v|`
C. `|uv|`
D. `2|uv|`

Explanation

To find the area of the triangle with vertices at the points \((u,0)\), \((v,8)\), and \((0,0)\), we can follow these steps:

### Step 1: Identify the vertices
The vertices of the triangle are given as:
- \( A(u, 0) \)
- \( B(v, 8) \)
- \( C(0, 0) \)

### Step 2: Determine the base and height of the triangle
In the coordinate plane:
- The base of the triangle can be considered as the horizontal distance from point \( C(0, 0) \) to point \( A(u, 0) \). Thus, the length of the base \( b \) is \( u \).
- The height \( h \) of the triangle is the vertical distance from point \( B(v, 8) \) to the line segment \( AC \) (which lies on the x-axis). Since point \( B \) has a y-coordinate of 8, the height \( h \) is 8.

### Step 3: Use the area formula for a triangle
The area \( A \) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Substituting the values we found:
\[ A = \frac{1}{2} \times u \times 8 \]

### Step 4: Simplify the expression
Now, simplify the expression:
\[ A = \frac{8u}{2} = 4u \]

### Step 5: Consider the absolute value
Since area cannot be negative, we express the area as:
\[ A = |4u| \]

### Final Answer
Thus, the area of the triangle is:
\[ \text{Area} = 4|u| \]