Richard A. answered • 05/27/19

Master of Science in Mathematics with 44+ years of teaching experience

The slope from (2,2) to (5,-4) is m=-2. The slope of the altitude to that side is the negative reciprocal which is 1/2. We can find the equation of the line through that altitude can be found using the slope of the altitude and the point (2,-5). Substituting the coordinates (4,-4) and the slope of 1/2 into y=mx+b produces -4=(1/2)4 + b. Solve for b to get -6. The equation of the line through the altitude is y = (1/2)x -6. The altitude from the point (2,2) to the line through the points (4,-4) and (5,-4) has an undefined slope because it is a vertical line. Therefore its equation is x=2. Substituting x=2 into the first equation produces y= (1/2)2 - 6 = -5. Therefore the intersection of the two altitudes occurs at the point (2,-5)