Question

Orthocentre of triangle whose vertices are $(0,0),(0,3),(4,0)$ is

• A. $(3,7/3)$
• B. $(3,5/4)$
• C. $(5,-2)$
• D. $(0,0)$

Answer 1

Answer: (D)

$(0,0)$

Given vertices forms a right triangle.

When the triangle is right, the orthocenter is the vertex of the triangle at the right angle. Intuitively this makes sense because the orthocenter is where the altitudes intersect. Hence, in a right triangle, the vertex of the right angle is where you would expect the altitudes to meet, at 90 degrees, where the legs of the right triangle are perpendicular.

Since$(0,0);(3,0);(0,4)$is a right triangle, the ${90}^o$ deg vertex, $(0,0)$ is the orthocenter