Question

$(0,0),(0,3)$ and $(3,0)$ form ___________.

• A. a straight line
• B. an equilateral triangle
• C. a scalene triangle
• D. a right triangle

Answer 1

The correct option is D a right triangle

Let the vertices be $A(0,0)$, $B(0,3)$ and $C(3,0)$. Now the measure of sides are
$AB=3$ units
$BC=\sqrt{(0-3{)}^2+(3-0{)}^2}=\sqrt{3^2+3^2}=3\sqrt{2}units$.
$AC=3$ units.
Hence, we can observe that $A{B}^2+A{C}^2=3^2+3^2=2\left(3^2\right)=B{C}^2$.

Thus, it follows Pythagoras theorem with BC being the hyptenuse and AC and AB being the perpendicular sides.

Hence, the above vertices form a right angled triangle.