Question

if A( 4, 3 ),B( - 1, Y) ,C ( 3, 4) are the vertices of a right angletriangle ABC .angle A is equal to 90 degree find the value of y​

Answer 1

Solution: H² = B² + P²

→ BC² = AB² + AC²

Distance Formula

→ √[(x₂ - x₁)² + (y₂ - y₁)²]

BC² → (- 1 - 3)² + (y - 4)² = 16 + y² + 16 - 8y

AB² → (4 + 1)² + (3 - y)² = 25 + 9 + y² - 6y

AC² = (4 - 3)² + (3 - 4)² = 2

• H² = 16 + y² + 16 - 8y
• P² = 25 + 9 + y² - 6y
• B² = 2

→ 16 + y² + 16 - 8y = 25 + 9 + y² - 6y + 2

→ 32 - 8y = 34 - 6y + 2

→ - 4 = 2y

→ - 2 = y

Hence value of y is - 2

Answer 2

||✪✪ QUESTION ✪✪||

if A( 4, 3 ),B( - 1, Y) ,C ( 3, 4) are the vertices of a right angletriangle ABC .angle A is equal to 90 degree find the value of y ?

|| ★★ FORMULA USED ★★ ||

→ In a Right Angled ∆, Side opposite to 90° is called as Hypotenuse..

→ Pythagoras Theoram :-

(Base)² + (Perpendicular)² = (Hypotenuse)²

→ Distance b/w Two points (x1,y1) and (x2,y2) is given by :-

√(x2-x1)² + (y2-y1)²

→ (a-b)² = a² + b² - 2ab

_____________________________

|| ✰✰ ANSWER ✰✰ ||

It is given that Angle A is Equal to 90° in Right angled ∆ABC,

So, we can say that, Side BC opposite to 90° is our Hypotenuse..

Hence, By Pythagoras Theoram we have :-

→ AB² + AC² = BC² ----- Equation(1)

Now, Given :-

→ A = (4,3)

→ B = (-1,y)

→ C = (3,4)

So,

→ AB = √[(-1-4)² + (y-3)²] ---------- Equation (2)

→ AC = √[(3-4)² + (4-3)²] ---------- Equation (3)

→ BC = √[(3-(-1))² + (4-y)²] ---------- Equation (4)

___________________________

Now, Squaring Equation (2),(3) and (4) and Putting in Equation (1) , we get,

→ [(-1-4)² + (y-3)²] + [(3-4)² + (4-3)²] = [(3-(-1))² + (4-y)²]

→ [ (-5)² + (y-3)²] + [(-1)² + 1²] = [(4)² + (4-y)²]

→ [ 25 + y² + 9 - 6y] + [ 1 + 1] = [ 16 + 16 + y² - 8y ]

→ y² - 6y + 36 = y² - 8y + 32

y² will be cancel From both sides ,

→ (-6y) + 8y = 32 - 36

→ 2y = (-4)

Dividing both sides by (-2)

→ y = (-2) .

Hence, value of y is (-2) .