Answer:
(2, 5)
Step-by-step explanation:
The orthocenter is the point where the altitudes intersect. For an obtuse triangle, it is outside the triangle. A graph of the triangle can help you find it.
One side of the triangle is the horizontal line y=4, so the vertical line through the opposite vertex will pass through the orthocenter. That line is x=2.
The side XY has a "rise" of -1 for each "run" of 1, so its slope is ...
rise/run = -1/1 = -1
Then the orthocenter will be on the line through point Z that has a slope equal to +1. A point that is on the line x=2 is 1 unit to the right of point Z, so will be one unit up from point Z, at (2, 5).
The orthocenter of this triangle is at (2, 5).
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The slopes of perpendicular lines have a product of -1.
