The coordinates of angular point of a `Delta ` ABC are A(0,1), B(2,0) and C(-1,-2). Find the equation of side AB of the triangle.

Options

A. x-2y=1
B. x + y = 2
C. x + 2y = 2
D. x + 3y = 1

Answer

To find the equation of side AB of triangle ABC with vertices A(0, 1) and B(2, 0), we can use the two-point form of the equation of a line.

### Step-by-step solution:

1. **Identify the coordinates of points A and B**:
- A(0, 1) → (x1, y1) = (0, 1)
- B(2, 0) → (x2, y2) = (2, 0)

2. **Use the two-point form of the equation of a line**:
The equation of a line passing through two points (x1, y1) and (x2, y2) can be expressed as:
\[ y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1) \]

3. **Substitute the coordinates into the equation**:
\[ y - 1 = \frac{0 - 1}{2 - 0}(x - 0) \]
Simplifying the right side:
\[ y - 1 = \frac{-1}{2}x \]

4. **Rearranging the equation**:
To eliminate the fraction, multiply both sides by 2:
\[ 2(y - 1) = -x \]
Expanding this gives:
\[ 2y - 2 = -x \]

5. **Rearranging to standard form**:
Adding x to both sides:
\[ x + 2y - 2 = 0 \]
Thus, the equation can be written as:
\[ x + 2y = 2 \]

### Final Answer:
The equation of side AB of triangle ABC is:
\[ x + 2y = 2 \]