The points (−4, 0), (4, 0), (0, 3) are the vertices of a:

Solution:

Let the vertices be A(−4, 0), B(4, 0), and C(0, 3). We compute squared side lengths to avoid square roots.

• AB^2 = (4 − (−4))^2 + (0 − 0)^2 = 8^2 + 0 = 64

• AC^2 = (0 − (−4))^2 + (3 − 0)^2 = 4^2 + 3^2 = 16 + 9 = 25

• BC^2 = (0 − 4)^2 + (3 − 0)^2 = (−4)^2 + 3^2 = 16 + 9 = 25

From these, AC = BC = 5 and AB = 8, so two sides are equal.

Check if the triangle is right-angled: AC^2 + BC^2 = 25 + 25 = 50, which is not equal to AB^2 = 64, so the triangle is not right-angled.

Conclusion: The triangle has exactly two equal sides, so it is an isosceles triangle. It is not equilateral because not all three sides are equal, and it is not right-angled.