Q.

Find the orthocentre of the triangle with the vertices (–5, –7), (13, 2) & (–5, 6)

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Detailed Solution

Let A(–5, –7), B(13, 2) and C(–5, 6) be the given vertices

 Let AD¯BC¯
 Slope of BC¯=2/9

 Let AD¯BC¯ then

slope of AD=92
 Equation of AD¯ is y(7)=92(x(5)
9x2y+31=0 ....(1)
 And BE¯AC¯, slope of AC¯=6+75+5=130
 Equation of BE¯ is y2=013(x13)y=2 ....(2)
Solve (1) & (2) x = –3, y = 2
orthocentre of the triangle  is (–3, 2)

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