Question

The points A(5, 5), B(4, 4) and C(3, 3) are joined to form a shape.
What type of triangle will be formed if the points are joined ?

• A. Equilateral triangle
• B. Isosceles triangle
• C. Scalene triangle
• D. The three points do not form a triangle

Answer 1

The correct option is D The three points do not form a triangle

We can use the distance formula to find the distances between the points, thereby finding what 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 do not form any triangle.