Question

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​

Answer 1

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...☺