Respuesta :
Steve claims that the points (-4,8) (8,8) and (-4,3) form a right triangle. Yes, Steve is correct.
What is the Pythagoras theorem?
The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
As we know the distance between (a, b) and (c, d) is:
distance = √( (a - c)² + (b - d)²)
The distance between (-4, 8) and (8, 8) is:
d₁ = √( (-4 - 8)² + (8- 8)²) = 12
The distance between (8, 8) and (-4, 3) is:
d₂ = √( (8 + 4)² + (8- 3)²) = 13
The distance between (-4, 8) and (-4, 3) is:
d₃ = = √( (-4 + 4)² + (8 - 3)²) = 5
If the Pythagorean theorem is correct, then the square of the larger side must equal the sum of the squares of the two shorter sides, which means that:
5² + 12² = 13²
Solving that we get:
25 + 144 = 169
169 = 169
Thus, Steve claims that the points (-4,8) (8,8) and (-4,3) form a right triangle. Yes, Steve is correct.
Learn more about Pythagoras' theorem here:
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