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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