Triangle Area Calculation Using Vertices

The question asks for the area of a triangle formed by the vertices $(1, 0)$, $(-1, 0)$, and $(0, 1)$. We can calculate this using the base and height method, as the base conveniently lies on the x-axis.

Identify Base and Height

• Vertices: Let the vertices be $A = (1, 0)$, $B = (-1, 0)$, and $C = (0, 1)$.
• Base: The segment AB lies on the x-axis. The length of the base is the distance between A and B.
  Base length $= |x_A - x_B| = |1 - (-1)| = |1 + 1| = 2$ units.
• Height: The height is the perpendicular distance from vertex C to the base (the x-axis). This is the absolute value of the y-coordinate of C.
  Height $= |y_C| = |1| = 1$ unit.

Calculate Triangle Area

Use the standard formula for the area of a triangle:

Area $= \frac{1}{2} \times \text{Base} \times \text{Height}$

Substitute the calculated values:

Area $= \frac{1}{2} \times 2 \times 1$

Area $= 1$ sq. unit.

Conclusion

The area of the triangle formed by the given vertices is 1 sq. unit.