Δabc has vertices a(0,10), b(4,10), and c(-2,4). find the orthocenter of δabc. question 6 options: a (2, -12) b (12, -2) c (-2, -12) d (-2, 12)

The orthocenter is the point of intersection of the altitude lines of the triangle. Of course, each altitude line is perpendicular to a side and passes through the vertex opposite.

A graphing program shows the appropriate choice to be
  d (-2, 12)

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Here, the answer choices are sufficiently far apart that you can pick the appropriate one "by eye." No calculations are necessary. The altitude lines to segments AB and BC must intersect in the second quadrant. Only one answer choice lies there.