Let, the given vertices be A(x1, y1) = (8, 2),
B(x2, y2) = (5, – 3) and C(x3, y3) = (0, 0)
∴ AB = \(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)
= \(\sqrt{(8-5)^2+(2+3)^2}\) =\(\sqrt{34}\) units.
C =\(\sqrt{(x_2-x_3)^2+(y_2-y_3)^2}\)
= \(\sqrt{(5-0)^2+(-3-0)^2}\) = \(\sqrt{34}\) units.
∴ AB = BC (⇒ ∠ACB = ∠BAC).
Hence, ∆ABC is isosceles.