We have given three points of a triangle.

Given: A(0, 4), B(1, 2), C(3, 3)

To Prove: Given points are the vertices of Right – angled Triangle.

Proof: We have A(0, 4), B(1, 2), C(3, 3)

The concept used: If the two lines are perpendicular to each other then it will be a right – angled triangle.

Now, Joining the points to make a line as AB, BC, and CA

The formula used: The slope of the line, m =

Now, The slope of line m_AB =

The slope of m_AB =

and, The slope of line BC =

The slope of m_Bc =

Now, m_AB × m_Bc =

m_AB × m_Bc = – 1

Since, AB is perpendicular to BC, it means B =

Hence, ABC is a right angle Triangle.