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k/find the orthocenter of the triangle with the following vertices(-2,-1), (6,-1) and (2,5) |
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Answer» By inspection, we see that the base of the triangle formed by the vertices (-2,-1) and (6,-1) is symmetric about the line x=2,so this altitude goes through the point (2,-1), and we know the x coordinate of the orthocentre is 2.To find the y coordinate, we use the fact that an altitude will be perpendicularto the line formed by any two vertices, and will pass through the 3rd vertex.Using (6,-1) and (2,5), the line isy + 1 = ((5+1)/(2-6)(x - 6) -> y = -3/2x + 8And, since perpendicular lines have negative reciprocal slope, the line for the altitude isy + 1 = 2/3(x + 2) -> y = 2/3x + 1/3The intersection point of x = 2 and y = 2/3x + 1/3 gives the orthocentrey = 2/3*2 + 1/3 = 5/3Ans: (2,5/3) |
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