# The equation of an altitude of an equilateral triangle is  and one of the vertices is   The possible number of triangle is   a) 1 b) 2 c) 3 d) 4

## Question ID - 55405 :- The equation of an altitude of an equilateral triangle is  and one of the vertices is   The possible number of triangle is   a) 1 b) 2 c) 3 d) 4

3537

Answer Key : (b) -

(b)

Let the triangle be  with  and altitude drawn through vertex (meeting  at ) be . If  is , then we have

And coordinates of  is . Let coordinates of vertex  be . Then,

Hence, the remaining vertices are (0, 0) and  or  and . Also, the orthocenter is  or (2, 0)

Next Question :
 For points  and  of the coordinate plane, a new distance  is defined by . Let  and . Consider the set of points  in the first quadrant which are equidistant (with respect to the new distance) from  and The set of points  consists of a) One straight line only b) Union of two line segments c) Union of two infinite rays d) Union of a line segment of finite length and an infinite ray