Question

A(1,7), B(2,4), C(k,5) are the vertices of a right angled ΔABC,Find k, if ∠A is a right angle

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.

Hope this helps!

Answer 2

In the attachment I have answered this problem.

Concept:

1. If two lines are perpendicular then

product of their slopes is equal to -1

2. Slope of line joining the two points
(x1, y1) and (x2, y2) is

(y2-y1) / (x2 - x1)

I hope this answer helps you