A(1, 7), B (2, 4) and C (k, 5) are the vertices
of a right triangle. Find k.
(1) if angleA = 90°, ( 2 ) if angleB = 90° and
(3) if angleC = 900
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Given A(1,7), B(2,4), C(k,5) are the vertices of Right angled triangle at A.
By Pythagoras theorem,
➲ AB^2 + AC^2 = BC^2
➲ [(2-1)^2 + (4-7)^2] + [(k-1)^2 + (5 - 7)^2] [(k-2)^2+(5-4)^2]
➲ 1 + 9 + k^2 +1-2k + 4 = k^2 + 4 - 4k + 1
➲ 15+ k^2 - 2k k^2 - 4k + 5
➲ k^2 - 2k = k^2 - 4k - 10
➲ 2k = -10
➲ k = -5.
Therefore, the value of k = -5.
I hope it's help you...☺
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