Question

8. If A (4, 3), B(-1,y) and C(3,4) are the vertices of right triangle ABC, right-angled at A, then find the value of y.

Answer 1

AB² + AC² = BC²
[(4+1)² + (3-y)²] + [(4-3)² + (3-4)²] = (-1-3)² + (y-4)²
25 + (3-y)² + 1 + 1 = 16 +(y-4)²
25+9+y²-6y+2 = 16+y²+16-8y
2y = 32-36
y = -2

Answer 2

Answer:

The Answer :- y = -2

Step-by-step explanation:

By Pythagoras Theorem :-

BC^2 = AB^2 + AC^2

_/ (16+16-8y+y^2) = _/ (25+y^2-6y+9 +  _/2

Square Both The Sides\

=> 16+16-8y+y^2 = 25+y^2-6y+9+2

=>  32-8y+6y = 36+y^2-y^2

=> 32-2y = 36+0

=>  32-2y-36 = 0

=> -2y = 36-32

-2y = 4

y = -4/2

y = -2

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