Question

The points A(−4, 0), B(4, 0) and C(0, 3) are the vertices of a triangle, which is

(a) isosceles
(b) equilateral
(c) scalene
(d) right-angled

Answer 1

(a) isosceles
Let A(−4, 0), B(4, 0) and C(0, 3) be the given points. Then,
$$\begin{gathered} AB=\sqrt{{\left(4+4\right)}^2+{\left(0-0\right)}^2} \\ =\sqrt{{\left(8\right)}^2+{\left(0\right)}^2} \\ =\sqrt{64+0} \\ =\sqrt{64} \\ =8\text{units} \\ BC=\sqrt{{\left(0-4\right)}^2+{\left(3-0\right)}^2} \\ =\sqrt{{\left(-4\right)}^2+{\left(3\right)}^2} \\ =\sqrt{16+9} \\ =\sqrt{25} \\ =5\text{units} \\ AC=\sqrt{{\left(0+4\right)}^2+{\left(3-0\right)}^2} \\ =\sqrt{{\left(4\right)}^2+{\left(3\right)}^2} \\ =\sqrt{16+9} \\ =\sqrt{25} \\ =5\text{units} \end{gathered}$$
BC = AC = 5 units
Therefore, $∆ABC$ is isosceles.