McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
Preparing for Standardized Tests
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Exercise 3 Page 387

Let's label the vertices and count squares to find the coordinates of the vertices. The orthocenter is the point of concurrency of the altitudes. Since the line through and is horizontal, the corresponding altitude must be vertical.

The orthocenter is on this vertical line, so the first coordinate must be Thus, answer choices A and B are certainly not correct. To choose between C and D let's consider another altitude.

If is the orthocenter, then is perpendicular to We know that the slopes of perpendicular lines multiply to so let's calculate the slope of and for the two possible in answer choices C and D.

Points Expression of the Slope Slope
and
and
and
We can see, that so is not the orthocenter of the triangle. This eliminates answer choice D, so the correct answer is the remaining answer C,

Alternative Solution

Alternative way of thinking

In the solution above we eliminated choices until only one left. Another way of finding the answer is to calculate the equation of two altitudes and work out the intersection point. This method is used for exactly this triangle in Example 4 of the book on page 338.