First slide

Pair of straight lines

Question

The orthocenter of the triangle formed by the lines x y = 0 and x + y = 1 is

Easy

A

(1/2,1/2)
B

(1/3,113)
C

(0, 0)
D

(1/4,1/4)

Solution

The lines by which triangle is formed are $x = 0, y = 0, x + y = 1$ . Clearly, it is a right triangle.
We know that in a right angled triangle, the orthocenter coincides with the vertex at which right angle is formed.
Therefore, the orthocenter is (0, 0).

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