Question

Find the orthocentre of with vertex a (– 7, 1), b (5, – 5), c (1, 7).

Answer 1

let, a=(-7,1)=(x1,y1)

b=(5,-5)=(x2,y2)

c=(1,7)=(x3,y3)

orthocentre is centroid

$centroid = ( \frac{x1 + x2 + r3}{3} + \frac{y1 + y2 + y3}{3} ) \\ \\ = ( \frac{ - 7 + 5 + 1}{3} + \frac{1 + ( - 5) + 7}{3} ) \\ \\ = ( \frac{ - 1}{3} + \frac{3}{3} ) \\ \\ = \frac{ - 1 + 3}{3} \\ \\ = \frac{2}{3}$
orthocentre = 2/3

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Answer 2

the answer is (x,y)=(-1,3)