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Which of the following sets of points are vertices of a right triangle?

1) A(-1, -3), B(4, -3), C(2, -1)
2) A(-2, 2), B(1, -4), C(4, 2)
3) A(-1, 1), B(3, 5), C(4, -4)
4) A(-1, 3), B(-4, -3), C(-4, 1)

1 Answer

3 votes

I scanned for a pair of x coordinates that match and a pair of y coordinates that match. That would be a right triangle whose sides are parallel to the axes. It's possible our right triangle is more complicated, but let's start here.

Nope, it doesn't look like our right triangle is oriented to the axes. Let's do the Pythagorean Theorem.

1) A(-1, -3), B(4, -3), C(2, -1)

AB² = (4 - -1)² + (-3 - -3)² = 25

AC²= (2 - -1)² + (-1 - -3)² = 9 + 4 = 13

BC²= (2 - 4)² + (-1 - -3)² = 4 + 4 = 8

25 ≠ 13 + 8, not a right triangle

2) A(-2, 2), B(1, -4), C(4, 2)

AB² = (-2 - 1)² + (-4 - 2)² = 9 + 36 = 45

AC²= (4 - -2)² + (2 - 2)² = 36

BC²= (4 - 1)² + (2 - -4)² = 9 + 36 = 45

not a right triangle, but isosceles

3) A(-1, 1), B(3, 5), C(4, -4)

AB² = 4² + 4² = 32

AC²= 5² + 5² = 50

BC²= 1² + 9² = 82

BC² = AC² + AB², THIS IS A RIGHT TRIANGLE

4) A(-1, 3), B(-4, -3), C(-4, 1)

AB² = 3² + 6² = 45

AC²= 3² + 2² = 13

BC²= 0² + 4² = 16

not a right triangle

Answer: 3) A(-1, 1), B(3, 5), C(4, -4)

User Erbdex
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