If lines are drawn from the point `(-5, 3)` to the coordinate axes then area of quadrilateral formed by these lines with coordinate axes is

Options

A. `(15)/(2)`
B. `15`
C. `30`
D. `(25)/(2)`

Answer

To find the area of the quadrilateral formed by drawing lines from the point (-5, 3) to the coordinate axes, we can follow these steps:

### Step 1: Identify the coordinates
The given point is (-5, 3). This means that the point is located 5 units to the left of the origin (on the x-axis) and 3 units above the origin (on the y-axis).

### Step 2: Draw lines to the axes
From the point (-5, 3), draw a vertical line down to the x-axis and a horizontal line to the y-axis. The vertical line will intersect the x-axis at (-5, 0) and the horizontal line will intersect the y-axis at (0, 3).

### Step 3: Identify the vertices of the quadrilateral
The quadrilateral formed by these lines and the coordinate axes has the following vertices:
- Point A: (-5, 0) (intersection with the x-axis)
- Point B: (0, 3) (intersection with the y-axis)
- Point C: (0, 0) (the origin)
- Point D: (-5, 3) (the original point)

### Step 4: Calculate the lengths of the sides
The lengths of the sides of the quadrilateral can be determined as follows:
- The horizontal distance from (-5, 0) to (0, 0) is 5 units.
- The vertical distance from (0, 0) to (0, 3) is 3 units.

### Step 5: Calculate the area
The area of the quadrilateral can be calculated using the formula for the area of a rectangle (since the shape formed is a rectangle):
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Here, the length is 5 units and the breadth is 3 units.
\[ \text{Area} = 5 \times 3 = 15 \text{ square units} \]

### Conclusion
The area of the quadrilateral formed by the lines drawn from the point (-5, 3) to the coordinate axes is **15 square units**.

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