A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, - 5) is the mid-point of PQ, then the coordinates of P and Q are respectively

Options

A. (0, - 5) and (2, 0)
B. (0, 10) and (- 4, 0)
C. (0, 4 )and ( -10, 0)
D. (0, - 10) and (4, 0)

Answer

To find the coordinates of points P and Q where a line intersects the y-axis and x-axis respectively, given that (2, -5) is the midpoint of PQ, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coordinates of P and Q**:
- Let the coordinates of point P (where the line intersects the y-axis) be (0, p).
- Let the coordinates of point Q (where the line intersects the x-axis) be (q, 0).

2. **Use the Midpoint Formula**:
- The midpoint M of a line segment connecting points (x1, y1) and (x2, y2) is given by:
\[ M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) \]
- Here, the midpoint M is given as (2, -5). Therefore, we can set up the equations:
\[ \frac{0 + q}{2} = 2 \quad \text{(for the x-coordinate)} \]
\[ \frac{p + 0}{2} = -5 \quad \text{(for the y-coordinate)} \]

3. **Solve for q**:
- From the first equation:
\[ \frac{q}{2} = 2 \implies q = 2 \times 2 = 4 \]

4. **Solve for p**:
- From the second equation:
\[ \frac{p}{2} = -5 \implies p = -5 \times 2 = -10 \]

5. **Determine the Coordinates of P and Q**:
- Now we have:
- Point P (0, p) = (0, -10)
- Point Q (q, 0) = (4, 0)

### Final Answer:
The coordinates of P and Q are respectively (0, -10) and (4, 0).