Q. 104.5( 12 Votes )

Without using Pythagoras theorem, show that the points A(0, 4), B(1, 2), C(3, 3) are the vertices of a right – angled triangle.

Answer :

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 mAB =


The slope of mAB =


and, The slope of line BC =


The slope of mBc =


Now, mAB × mBc =


mAB × mBc = – 1


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


Hence, ABC is a right angle Triangle.


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