# 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.

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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