Question

Can the following points form a triangle?
A(5, 5), B(4, 4) and C(3, 3)
If yes, which triangle it could be?

• A. Isosceles
• B. Scalene
• C. Right angled
• D. The three points don’t form a triangle.

Answer 1

The correct option is D

The three points don’t form a triangle.

Distance formula can be used to find the distance between points.

The given points are- A(5, 5), B(4, 4) and C(3, 3).

Using the distance formula we get,

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

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

We can also see that BC + AB = AC.

Now, in any triangle, the sum of any two sides must be greater than the third side.

Since this condition is not satisfied, the points do not form any triangle.