Question

Can the following points form a triangle?
A(5, 5), B(4, 4), and C(3, 3)
If yes, what type of triangle will it be?

Answer 1

A(5, 5), B(4, 4), and C(3, 3)
Distance between $(x_1,y_1)and(x_2,y_2)=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

Using the distance formula we get,

$AC=\sqrt{(5-3{)}^2+(5-3{)}^2}=\sqrt{4+4}=2\sqrt{2}units$
$BC=\sqrt{(4-3{)}^2+(4-3{)}^2}=\sqrt{1+1}=\sqrt{2}units$
$AB=\sqrt{(5-4{)}^2+(5-4{)}^2}=\sqrt{1+1}=\sqrt{2}units$

$\Rightarrow$The length of two sides are equal, i.e., AB = BC.

We can also see that BC + AB = AC.

Since, in any triangle, the sum of any two sides is greater than the third side. So, the points do not form any triangle.