Question

A question was asked in a class:
”The points A(5, 5), B(4, 4) and C(3, 3) form what kind of a triangle?”
Unfortunately, no student could get it right.
What kind of triangle would the three points form?

• 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

We can use the distance formula to find
the distances between the points,
thereby finding the type of triangle it is.

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

Using the distance formula we have,

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

The length of two sides are equal, $AB=BC$.

We 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 cannot form a triangle.