. Do the points P (-2, -3), Q (4, 1) and R (2, 4) form a right triangle?

Since the length of the sides respects the Pythagorean theorem, these points form a right triangle.

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, and . The distance between them is given by:

Right triangle:

Sum of the squares of the two smaller sides is equal to the square of the largest side(Pythagorean theorem).

Length of side PQ:

P (-2, -3), Q (4, 1)

Length of side PR:

P (-2, -3), R (2,4)

Length of side QR

Q (4, 1), R (2,4)

Pythagorean Theorem:

Smaller sides: a and c

Largest side: b

So

Since the length of the sides respects the Pythagorean theorem, these points form a right triangle.

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