Saved Bookmarks
| 1. |
The points A(– 4, 0), B(4, 0) and C(0, 3) are the vertices of a triangle. Is the triangle isosceles? Show by calculations. |
|
Answer» Given that the vertices of a triangle ABC are A(–4, 0), B(4, 0) and C(0, 3). The side length of AB = \(\sqrt{(4-(-4))^2+(0-0)^2}\) = \(\sqrt{(4+4)^2+0}\) = 8 unit. (By distance formula between two points) The side length of BC = \(\sqrt{(0-4)^2+(3-0)^2}\) = \(\sqrt{16+9}\) = \(\sqrt{25}\) = 5 unit. The side length of AC = \(\sqrt{(0-(-4))^2+(3-0)^2}\) = \(\sqrt{16+9}\) = \(\sqrt{25}\) = 5 unit. Hence, BC = AC = 5 unit in triangle ABC. ∴ Triangle ABC is an isosceles triangle. Hence Proved |
|