Question

Graphically, the two systems of equations \(x+7=0, y-2=0\) and \(x-2=0, y+7=0\) enclose a :

• A. Square region
• B. Rectangular region
• C. A triangular region
• D. Trapezium shaped region

Hint:

1. Identify the lines: \(x=-7\), \(y=2\), \(x=2\), \(y=-7\). 2. These are two vertical and two horizontal lines. They will form a rectangle (or a square). 3. Width of the rectangle (distance between \(x=-7\) and \(x=2\)) = \(|2 - (-7)| = 9\). 4. Height of the rectangle (distance between \(y=-7\) and \(y=2\)) = \(|2 - (-7)| = 9\). 5. Since width = height = 9, the figure is a square.

Answer 1

The Correct Option is A

Concept: Each equation represents a line. We need to identify these lines and the shape they form. Step 1: Identify the four lines
From first system: \(x+7=0 \implies x = -7\) (Vertical line) \(y-2=0 \implies y = 2\) (Horizontal line)
From second system: \(x-2=0 \implies x = 2\) (Vertical line) \(y+7=0 \implies y = -7\) (Horizontal line) Step 2: Visualize or sketch the lines These four lines are \(x=-7, x=2, y=2, y=-7\). Vertical lines pass through \(x=-7\) and \(x=2\). Horizontal lines pass through \(y=2\) and \(y=-7\). Step 3: Determine the properties of the enclosed shape The lines form a quadrilateral.
The horizontal sides are bounded by \(x=-7\) and \(x=2\). The length of these sides is \(|2 - (-7)| = |2+7| = 9\) units.
The vertical sides are bounded by \(y=2\) and \(y=-7\). The length of these sides is \(|2 - (-7)| = |2+7| = 9\) units. Since horizontal lines are perpendicular to vertical lines, all angles of the enclosed quadrilateral are \(90^\circ\). The lengths of all four sides are equal (9 units). A quadrilateral with four right angles and four equal sides is a square. Step 4: Conclusion The lines enclose a square region. "Square region" is the most specific correct description. (A square is also a rectangle, but "square" is more precise). The circled option (3) "A triangular region" in the original image is incorrect as four lines typically form a quadrilateral.