Yes, the points are the vertices of a right triangle and we will prove that by using the Pythagorean theorem.
Remember that the distance between two points (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 true, then the sum of the squares of the two shorter sides must be equal to the square of the larger side, then we must have that:
5² + 12² = 13²
Solving that we get:
25 + 144 = 169
169 = 169
This is true, so yes, the vertices are the vertices of a right triangle.
Learn more about right triangles:
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