Discussion

A triangle with vertices at (0,0), (4,0), and (2,3) is a/an:

Answer: B

We use the distance formula \(\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\) to find the lengths of the sides.

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

Side 2 (between (0,0) and (2,3)): \(\sqrt{(2-0)^2 + (3-0)^2} = \sqrt{4+9} = \sqrt{13}\).

Side 3 (between (4,0) and (2,3)): \(\sqrt{(2-4)^2 + (3-0)^2} = \sqrt{(-2)^2+3^2} = \sqrt{4+9} = \sqrt{13}\).

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

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