Let A = (1, -3), B = (6, 2) and C = (0,4) \(d =\sqrt{ (y_2 - y_1)^2 + (x_2 - x_1)^2}\) |AB| = \(\sqrt{(2 - (-3))^2 + (6 - 1)^2}\) = \(\sqrt{(2 + 3)^2 + (6 - 1)^2}\) = \(\sqrt{5^2 + 5^2}\) = \(\sqrt{25 + 25}\) = \(\sqrt50\) = 5\(\sqrt2\) units |BC| = \(\sqrt{(4 - 2)^2 + (0 - 6)^2}\) = \(\sqrt{2^2 + (-6)^2}\) = \(\sqrt{4 + 36}\) = \(\sqrt40\) = 2\(\sqrt10\) units |AC| = \(\sqrt{(4 - (-3)^2 + (0 - 1)^2}\) = \(\sqrt{(4 + 3)^2 + (0 - 1)^2}\) = \(\sqrt{7^2 + (-1)^2}\) = \(\sqrt{49 + 1}\) = \(\sqrt50\) = 5\(\sqrt{2}\) units Since two sides are equal (|AB| = |AC|), then the triangle is Isosceles.