Question

If the points of intersection of the coordinate axes and $|x + y| = 2$ form a rhombus, then its area is

• A. $8$
• B. $16$
• C. $2$
• D. $4$

Hint:

Use symmetry and geometric shape properties to compute area directly from diagonal intersections.

Answer 1

The Correct Option is A

The equation $|x + y| = 2$ represents two lines: $x + y = 2$ and $x + y = -2$
These intersect the axes at: $(2, 0), (0, 2), (-2, 0), (0, -2)$
These 4 points form a rhombus centered at origin
Diagonal lengths = distance between opposite vertices = $4$ and $4\sqrt{2}$
Area of rhombus = $\dfrac{1}{2} \cdot d_1 \cdot d_2 = \dfrac{1}{2} \cdot 4 \cdot 4 = 8$