Question

The vertex of an equilateral triangle is at
(2.-1) and the side opposite to it has the
equation x+y=2 then orthocentre of the
triangles is​

Answer 1

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Answer 2

The orthocentre of the triangle is (7/3, -2/3).

Given,

The vertex of an equilateral triangle is at (2.-1) and the side opposite to it has the equation x+y = 2.

To Find,

The orthocentre of the triangle.

Solution,

Using the formula of calculating the foot of perpendicular.

Let us assume that the foot of perpendicular is (h,k).

(h-2)/1 = (k+1)/1 = -(2-1-2)/(1+1)

(h-2) = (k+1) = 1/2

h-2 = 1/2

h = 2+1/2 = 5/2

k+1 = 1/2

k = -1/2

Now, orthocentre of the triangle will be

O = [(2*5/2+2)/3, (2*(-1/2)-1)/3]

O = (7/3, -2/3)

Hence, the orthocentre of the triangle is (7/3, -2/3).

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