Question

What kind of triangle is formed by joining points A(3, 2), B(4, 1), and C(5, 0)?

[1 mark]

• A. Equilateral triangle
• B. Isosceles triangle
• C. Right-angled triangle
• D. No triangle is formed

Answer 1

The correct option is D No triangle is formed

Using the distance formula,

Distance between A(3, 2) and B(4, 1) $=\sqrt{(1-2{)}^2+(4-3{)}^2}=\sqrt{2}$

Distance between B(4, 1) and C(5, 0) $=\sqrt{(0-1{)}^2+(5-4{)}^2}=\sqrt{2}$

Distance between A(3, 2) and C(5, 0) $=\sqrt{(0-2{)}^2+(5-3{)}^2}=2\sqrt{2}$

The length of the two sides AB and AC are equal.
AB + BC = AC

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

Since this condition is not satisfied, no triangle will be formed.