Question

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

Answer 1

Dear Student,

Solution:

If given points are vertex of right angle triangle,then we can apply Pythagoras theorem

AC² = AB²+BC²

now you have vertex of all three points, apply distance formula to calculate the distance of AB, AC and BC

AB = √{(2-1)² + (4-7)²} = √10

AB² = 10 -------eq1

BC = √{(2-k)² + (4-5)²} = √{(2-k)² +1}

BC² = (2-k)²+1 ----------eq2

AC = √{(1-k)² + (7-5)²} = √{(1-k)² +4}

AC² = (1-k)² +4------------eq3

Apply all distances into Pythagoras theorem

(1-k)² +4 = (2-k)²+1 +10

1 +k² -2k +4 = 4 +k²-4k+11

-2k +4k = 15-5

2k = 10

k = 10/2

k = 5

hence the point C is (5,5)

hope it helps you.

Answer 2

In the attachment I have answered this problem.

Concept:

1.The slope of line joining (x1, y1)

and (x2, y2) is (y2-y1)/(x2-x1)

2. If Two lines are perpendicular

then product of their slopes is equal

to -1.

See the attachment for detailed solution