Discussion

The points (1, 1), (3, 4), and (5, 1) are the vertices of a/an:

Answer: B

Let's find the lengths of the sides using the distance formula.

Side 1 (between (1,1) and (3,4)): \(\sqrt{(3-1)^2 + (4-1)^2} = \sqrt{2^2 + 3^2} = \sqrt{4+9} = \sqrt{13}\).

Side 2 (between (3,4) and (5,1)): \(\sqrt{(5-3)^2 + (1-4)^2} = \sqrt{2^2 + (-3)^2} = \sqrt{4+9} = \sqrt{13}\).

Side 3 (between (1,1) and (5,1)): \(\sqrt{(5-1)^2 + (1-1)^2} = \sqrt{4^2 + 0^2} = 4\).

Since two sides have the same length (\(\sqrt{13}\)), the triangle is isosceles.

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