MCQ
The points $(0, 3), (4, 0)$ and $(-4, 0)$ are the vertices of:
- ✓an isosceles triangle
- Ban equilateral triangle
- Ca right triangle
- Da scalene triangle
✓
Answer
Correct option: A.
an isosceles triangle
Let vertices of a triangle $\text{ABC}$ are $A(0, 3) B(-4, 0)$ and $C(4, 0).$
$\therefore\text{AB}=\sqrt{(-4-0)^2+(0-3)^2}$
$=\sqrt{16+9}=\sqrt{25}=\text{5 units}$
$\text{BC}=\sqrt{(4+4)^2+(0-0)^2}$
$=\sqrt{64+0}=\sqrt{25}=8\text{ units}$
$\text{AC}=\sqrt{(4-0)^2+(0-3)^2}$
$=\sqrt{16+9}=\sqrt{25}=\text{5 units}$
Since two sides are equal, therefore, $\text{ABC}$ is an isosceles triangle.
$\therefore\text{AB}=\sqrt{(-4-0)^2+(0-3)^2}$
$=\sqrt{16+9}=\sqrt{25}=\text{5 units}$
$\text{BC}=\sqrt{(4+4)^2+(0-0)^2}$
$=\sqrt{64+0}=\sqrt{25}=8\text{ units}$
$\text{AC}=\sqrt{(4-0)^2+(0-3)^2}$
$=\sqrt{16+9}=\sqrt{25}=\text{5 units}$
Since two sides are equal, therefore, $\text{ABC}$ is an isosceles triangle.
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