Question

DAM NAJJJJ.!!!!!

Sprawdź, czy trójkąt jest prostokątny.

a) A=(-5,0), B=(o,-2), C=(2,2)

b) A=(4,-1), B=(1,5), C=(7,-1)

c) A=(-3.-1) B=(6,-4), C=(7,-1)

Answer 1

a) A = (-5,0) B = (0,-2) C = (2,2)
|AB| = √(0 + 5)² + (-2 - 0)² = √5² + (-2)² = √25 + 4 = √29
|BC| = √(2 - 0)² + (2 + 2)² = √2² + 4² = √4 + 16 = √20
|AC| = √(2 + 5)² + (2 - 0)² = √7² + 2² = √49 + 4 = √53
|AC|² ≠ |AB|² + |BC|²
(√53)² ≠ (√29)² + (√20)²
53 ≠ 29 + 20
53 ≠ 49

 

NIE

 

b) A = (4,-1) B = (1,5) C = (-4,3)
|AB| = √(1 - 4)² + (5 + 1)² = √(-3)² + 6² = √9 + 36 = √45
|BC| = √(-4 - 1)² + (3 - 5)² = √(-5)² + (-2)² = √25 + 4 = √29
|AC| = √(-4 - 4)² + (3 + 1)² = √(-8)² + 4² = √64 + 16 = √80
|AC|² ≠ |AB|² + |BC|²
(√80)² ≠ (√45)² + (√29)²
80 ≠ 45 + 29
80 ≠ 74

 

NIE

 

c) A = (-3,-1) B = (6,-4) C = (7,-1)
|AB| = √(6 + 3)² + (-4 + 1)² = √9² + (-3)² = √81 + 9 = √90
|BC| = √(7 - 6)² + (-1 + 4)² = √1² + 3² = √1 + 9 = √10
|AC| = √(7 + 3)² + (-1 + 1)² = √10² + 0² = √100 + 0 = √100
|AC|² = |AB|² + |BC|²
(√100)² = (√90)² + (√10)²
100 = 90 + 10
100 = 100

 

TAK