Question

Determine X de modo que o triangulo ABC seja retangulo em B. São dos A(-2 5) B(2 -1) e C(3 X)? 

Answer 1

Oi 

AC² = AB² + BC²

AB² = (Ax - By)² + (Ay - By)²
AB² = (-2 - 2)² + (5 + 1)² = 16 + 36 = 52

BC² = (Bx - Cx)² + (By - Cy)²
BC² = (2 - 3)² + (-1 - x)² = 1 + x² + 2x + 1 = x² + 2x + 2

AC² = (Ax - Cx)² + (Ay - Cy)²
AC² = (-2 - 3)² + (5 - x)² = 25 + x² - 10x + 25 = x² - 10x + 50 

x² - 10x + 50 = 52 + x² + 2x + 2

-10x + 50 = 2x + 54 

12x = -4
x = -4/12 = -1/3