In triangle ABC, the sides BC, CA, and AB lie along the lines x - 2y + 5 = 0, x + y + 2 = 0, and 8x - y - 20 = 0 respectively. Find the orthocentre of triangle ABC.

(-3, 1)
(-1/3, 2/3)
(-2, 4)
(-2/3, 4/3)

Correct answer: (-1/3, 2/3)

Solution

Find vertices by intersecting pairs of lines, then construct two altitudes (perpendicular from each vertex to the opposite side), and solve for their intersection to get the orthocentre.

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