Question

(1) A (1, 7), B (2, 4) and C (k, 5) are the
vertices of A ABC and angle
A = 90°. Then
k= ..​

Answer 1

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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.