Question:
The orthocentre of the triangle formed by the axes and the line $x + y = 1$ is:
The orthocentre of the triangle formed by the axes and the line $x + y = 1$ is:
Show Hint
Right-angled triangle orthocentre = Right angle vertex; Circumcentre = Midpoint of hypotenuse.
Updated On: Apr 8, 2026
- $(0, 0)$
- $(1/2, 1/2)$
- $(1, 1)$
- $(1/3, 1/3)$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The orthocentre is the point of intersection of the altitudes of a triangle.
Step 2: Analysis
The triangle is formed by $x=0$ (y-axis), $y=0$ (x-axis), and $x+y=1$. This is a right-angled triangle.
Step 3: Conclusion
In a right-angled triangle, the orthocentre is the vertex containing the right angle. Here, that is the origin $(0, 0)$.
Final Answer: (A)
The orthocentre is the point of intersection of the altitudes of a triangle.
Step 2: Analysis
The triangle is formed by $x=0$ (y-axis), $y=0$ (x-axis), and $x+y=1$. This is a right-angled triangle.
Step 3: Conclusion
In a right-angled triangle, the orthocentre is the vertex containing the right angle. Here, that is the origin $(0, 0)$.
Final Answer: (A)
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