Question

If two vertices of a triangle are (0,2) and (4,3) and its orthocentre is (0,0) then the third vertex of the triangle lies in

(a) 1st quadrant
(b) 2ndquadrant
(c) 3rd quadrant
(d) 4th quadrant

Answer 1

The correct answer is option A. The third vertex of the triangle lies in the 1st quadrant.

Step-by-step explanation:

To find the third vertex of the triangle, we can use the fact that the orthocenter of a triangle is the intersection point of its altitudes. Since we know that the orthocenter is (0, 0), we can find the equations of the altitudes passing through the given vertices and then find their point of intersection. The equation of the altitude passing through (0, 2) is y = -x/2 + 2, and the equation of the altitude passing through (4, 3) is y = -3x/4 + 3. Solving these two equations, we find that the point of intersection is (8, 0). Therefore, the third vertex of the triangle lies in the 1st quadrant.