Question

Prove that the points A(6,7), B(– 2,3) and C(8,3) are vertices of a right angled triangle.​

Answer 1

Given to prove these are the vertices of right angle triangle:–

Explanation:–

A = (6,7 )

B = (-2,3)

C = (8,3)

Let's find the distance between the points by using Distance formula:-

= √(x₁-x₂)² +(y₁-y₂)²

A= (6,7) = (x₁, y₁)

B = (-2,3) = (x₂, y₂)

AB = √[6-(-2)]² + (7-3)²

AB = √(8)²+(4)²

AB = √64+16

AB = √80

AB = 4√5

B = (-2,3) = (x₁ , y₁)

C = (8,3) = (x₂, y₂)

BC = √(-2-8)²+(3-3)²

BC = √(-10)² +(0)²

BC = √100

BC = 10

C= (8,3)= (x₁ , y₁)

A= (6,7)= (x₂, y₂)

CA = √(8-6)² +(3-7)²

CA = √(-2)² +(-4)²

CA = √4 + 16

CA = √20

CA = 2√5

Now, Let's verify them by Pythagoras theorem .

AB² + CA² = BC²

(4√5 )² +(2√5 )² = (10)²

16(5) + 4(5) = 100

80+20 =100

100=100

Since ,it satisfies Pythagoras theorem

So, given vertices are vertices of Right angle triangle.

Hence proved ![tex][/tex]