Question

Answer the following with clear steps. (with reference to distance formula)

Answer 1

Given that it is a right angle triangle

⇒ a² + b² = c²

Find the length AB:

AB = √[ (3 - a)² + (0 + 2)² ]

AB = √[ 3² - 6a + a² + 2²]

AB = √(a² - 6a + 13)

Find the length BC:

BC = √[ (4 - a)² + (-1 + 2)² ]

BC = √[ 4² + a² - 8a + 1 ]

BC = √[ a² - 8a + 17 ]

Find the length AC:

AC = √[ (4 - 3)² + (-1 - 0)² ]

AC = √[ (1 + 1 ]

AC = √2

Solve a:

Given that the right angle is at vertex A

AB² + AC² = BC²

(√(a² - 6a + 13) )² +  (√2)² = ( √[a² - 8a + 17 ] )²

a² - 6a + 13 + 2 = a² - 8a + 17

2a = 2

a = 1

Answer: a = 1