The coordinates of the orthocenter of the triangle that has the coordinates of midpoints of its sides as (0,0),(1,2) and (−6,3) is

The coordinates of the orthocenter of the triangle that has the coordinates of midpoints of its sides as (0,0),(1,2) and (−6,3) is

Options

A. (0,0)
B. (−4,5)
C. (−5,5)
D. (−4,4)

Correct answer is option C.(−5,5). Explanation: We Know that ∠O = `90^0` (as AO⊥OB )

Hence P will be the orthocentre

AOBP forms a rectangle.
`\therefor` P = A + B − O (using the concept that diagonals bisect each other)
P (x,y) =
x = − 6 + 1 − 0 = −5
y = 2 + 3 − 0 = 5

Hence, The coordinates of the orthocenter of the triangle that has the coordinates of midpoints of its sides as (0,0),(1,2) and (−6,3) is (−5,5).