Question

The orthocentre of triangle formed by the points (1,0,(-1,0),and (0,√3) is

Answer 1

ans is given in attached pic

Answer 2

Solution :-

Let us assume that, the vertices of the given ∆ are A(1,0) , B(-1,0) and C(0, √3) .

so,

→ AB = √[(1+1)² + (0 - 0)²] = √(2)² = 2 unit

→ BC = √[(0+1)² + (√3 - 0)²] = √(1 + 3) = √4 = 2 unit .

→ CA = √[(0 - 1)² + (√3 - 0)²] = √(1 + 3) = √4 = 2 unit .

as we can see that,

→ AB = BC = CA .

then, we can conclude that, the given ∆ is an equaliteral ∆ .

now, we know that,

• In a equilateral triangle the circumcenter, incenter, centroid and orthocenter are at the same point .
• Centroid of a ∆ = (x1 + x2 + x3)/3 , (y1 + y2 + y3)/3

therefore,

→ Orthocentre of the ∆ = (1 - 1 + 0)/3 = 0/3 = 0 and (0 + 0 + √3)/3 = √3/3 .

hence, the orthocentre of the triangle are (0 , √3/3) .

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