Let the vertices of a triangle (0,0),(3,0) and (0,4) its orthocentre is

Options

A. (0,0)
B. `(1,4//3)`
C. `(3//2,3)`
D. None of these

Answer

To find the orthocenter of the triangle with vertices at (0,0), (3,0), and (0,4), we can follow these steps:

### Step 1: Identify the vertices of the triangle
The vertices of the triangle are:
- A = (0, 0)
- B = (3, 0)
- C = (0, 4)

### Step 2: Determine the type of triangle
We can observe that the triangle formed by these points is a right triangle. The right angle is at vertex A (0, 0), as the sides AB and AC are perpendicular to each other.

### Step 3: Understand the property of the orthocenter in a right triangle
In a right triangle, the orthocenter is located at the vertex where the right angle is. This is a special property of right triangles.

### Step 4: Identify the orthocenter
Since the right angle is at vertex A (0, 0), the orthocenter of the triangle is also at point A.

### Conclusion
Thus, the orthocenter of the triangle with vertices (0,0), (3,0), and (0,4) is at the point (0, 0).

### Final Answer
The orthocenter is at (0, 0).

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