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.
Similar Questions
- Find the relation between x and y such that the point (x, y) is equidistant from (6, 2) and (4, 6).
- The points A (1, 2), B (3, 4) and C (4, 1) are the vertices of a triangle which is:
- Three straight lines $x + y - 3 = 0$, $x + y + 2 = 0$ and $3x + 3y - 7 = 0$ are:
- The image of the point $(7, 8)$ when reflected along the x-axis is:
- The equation of a straight line passing through (-2,5) and (1,3) is:
- The intercepts made by the plane $3x - 4y - 2z = 6$ with the coordinate axis are:
- Find the relation between x and y such that the point (x, y) is equidistant from (5, 3) and (4, 6).
- The distance between two points $(a \cos \alpha, 0)$ and $(0, a \sin \alpha)$ is_____.
- The area of the triangle formed by the line $2x - 4y - 7 = 0$ with the coordinate axis is:
- The distance from the origin to the line $4x + 3y + 6 = 0$ is:
Important Questions from Coordinate Geometry
What is the reflection of the point (-1, 5) in the line x = 1?
What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?
Slope of the line AB is 4/3. Co-ordinates of points A and B are (x, -5) and (2, -3) respectively. What is the value of x?
Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
- If x² + y² - 12x + 18y + 117 = 0, then the value of x² + y² is:
